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• https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups — found via Wikipedia

  Classification of finite simple groups

  the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is

  List of finite simple groups the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie
  Group of Lie type of finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups. The
  Sporadic group classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups
  Simple group arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple groups, completed in 2004, is a major

• https://classificationoffinitesimplegroups.wordpress.com/ — found via User

  Classification of finite simple groups

  Much (if not all) of the proofs were publishied last century, to old for me to got an overview of the timeline on my own. Also I did not waste much time i…

• http://plus.maths.org/content/comment/8844 — found via Mwmbl

  An enormous theorem: the classification of finite simple groups …

  An enormous theorem: the classification of finite simple groups An enormous theorem: the classification of finite simple groups "In February 1981 the cla…

• http://arxiv.org/abs/1501.00135 — found via Mwmbl

  [1501.00135] Classification of finite simple amenable ${\cal Z}$…

  arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …

  [1210.6553] Classification of finite reparametrization symmetry … Title:Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model Abstract:Symmetries play a crucial role in electroweak …
  [1201.0272] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [1201.0272v2] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [1201.0272v1] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [1312.4246] Classification of finite-multiplicity symmetric pairs Title:Classification of finite-multiplicity symmetric pairs Abstract:We give a complete classification of the reductive symmetric pairs (G,H) for which t…
  [0810.2637] Classification of finite-growth general Kac-Moody su… Title:Classification of finite-growth general Kac-Moody superalgebras Abstract: A contragredient Lie superalgebra is a superalgebra defined by a Cartan m…
  [0901.1798] Classification of E_0--Semigroups by Product Systems Title:Classification of E_0--Semigroups by Product Systems Abstract:This paper presents the complete classification of E_0-semigroups by product systems …
  Classification and Feasibility Assessment of Infinitely Many Iso… Abstract In two-body dynamics, it is proven that for a sufficiently long flight time, generating infinitely many iso-impulse solutions is possible by sol…
  [1001.4556] Growth in finite simple groups of Lie type Title:Growth in finite simple groups of Lie type Abstract: We prove that if L is a finite simple group of Lie type and A a symmetric set of generators of…
  [1005.1858] Growth in finite simple groups of Lie type of bounde… Title:Growth in finite simple groups of Lie type of bounded rank Abstract:We prove that if L is a finite simple group of Lie type and A a symmetric set o…
  [1003.5611] Lie theory of finite simple groups and the Roth prop… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [1003.5611v3] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [1003.5611v4] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [1003.5611v2] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:We apply noncommutative differential geometry to finite nonabelian simple groups …
  [1309.1975] Expansion in finite simple groups of Lie type Abstract: We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the B…
  [1402.0341] Metric ultraproducts of finite simple groups Title:Metric ultraproducts of finite simple groups Abstract:Some new results on metric ultraproducts of finite simple groups are presented. Suppose that …
  [1001.5069] Expansion properties of finite simple groups Title:Expansion properties of finite simple groups Abstract: We prove that if G is SL_2(F) or PSL_2(F), where F is a finite field, and A is a set of gene…
  [0712.4069] The Bogomolov multiplier of finite simple groups Title:The Bogomolov multiplier of finite simple groups Abstract:The subgroup of the Schur multiplier of a finite group G consisting of all cohomology cla…
  [1907.10828] Short presentations of finite simple groups Title:Short presentations of finite simple groups Abstract:Guralnick, Kantor, Kassabov and Lubotzky (J. Eur. Math. Soc. 13.2, 2011, 391-458) [GKKL] give …
  [1003.5611v1] Lie theory of finite simple groups and the general… Abstract:We apply a recent approach to noncommutative differential geometry on finite groups to the case of finite nonabelian simple groups and similar g…
  [2003.00755v1] On the p-width of finite simple groups Title:On the p-width of finite simple groups Abstract:In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of …
  [2003.00755v2] On the p-width of finite simple groups Title:On the p-width of finite simple groups Abstract:In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of …
  [2406.17794] A characterization of some finite simple groups by … Title:A characterization of some finite simple groups by their character codegrees Abstract:For a finite group $G$ and an irreducible complex character $…
  [1603.04717] Generation of finite simple groups by an involution… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [0808.0622] On the Shortest Identity in Finite Simple Groups of … Title:On the Shortest Identity in Finite Simple Groups of Lie Type Abstract:We prove that the length of the shortest identity in a finite simple group of…
  [0903.0180] Classification of continuously transitive circle gro… Title:Classification of continuously transitive circle groups Abstract: Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant…
  [1603.04717v1] Generation of finite simple groups by an involuti… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [1603.04717v2] Generation of finite simple groups by an involuti… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [2109.02698v2] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [2109.02698v3] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [2109.02698v5] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [2109.02698v6] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [2109.02698v9] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [2109.02698v4] The essential p-dimension of finite simple groups… Title:The essential p-dimension of finite simple groups of Lie type Abstract:In this paper, we compute the essential p-dimension of the finite simple gro…
  [1104.1277] Classification of some countable descendant-homogene… Title:Classification of some countable descendant-homogeneous digraphs Abstract:For finite q, we classify the countable, descendant-homogeneous digraphs …
  [0810.0568] Finite simple groups with narrow prime spectrum Title:Finite simple groups with narrow prime spectrum Abstract: We find the nonabelian finite simple groups with order prime divisors not exceeding 1000.…
  [1001.0020] Classification of integrable hydrodynamic chains Title:Classification of integrable hydrodynamic chains Abstract: Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimen…
  [1901.00836] Word Maps in Finite Simple Groups Title:Word Maps in Finite Simple Groups Abstract:Elements of the free group define interesting maps, known as word maps, on groups. It was previously obs…
  [0810.0568v1] Finite simple groups with narrow prime spectrum Title:Finite simple groups with narrow prime spectrum Abstract: We find the nonabelian finite simple groups with order prime divisors not exceeding 1000.…
  [1409.7518] Which finite simple groups are unit groups? Title:Which finite simple groups are unit groups? Abstract:We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is i…
  [2312.15745] Finite almost simple groups whose holomorph contain… Abstract:In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In …
  [1911.02117] Simple groups with infinite verbal width and the sa… Abstract:In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abeli…
  [0808.0622v2] On the Shortest Identity in Finite Simple Groups o… Title:On the Shortest Identity in Finite Simple Groups of Lie Type Abstract:We prove that the length of the shortest identity in a finite simple group of…
  [1409.7518v1] Which finite simple groups are unit groups? Title:Which finite simple groups are unit groups? Abstract:We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is i…
  [2101.09071] Finitely presented simple groups and measure equiva… Title:Finitely presented simple groups and measure equivalence Abstract:We exhibit explicit infinite families of finitely presented, Kazhdan, simple grou…
  [2207.08788] Finite simple permutation groups acting with fixity… Abstract: Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we classify all finite simple groups that h…
  [1811.05343] Totally orthogonal finite simple groups Title:Totally orthogonal finite simple groups Abstract:We prove that if $G$ is a finite simple group, then all irreducible complex representations of $G$…
  [0910.5402] New Beauville surfaces and finite simple groups Title:New Beauville surfaces and finite simple groups Abstract:In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belo…
  [2407.16926] Commuting Involutions in Finite Simple Groups Title:Commuting Involutions in Finite Simple Groups Abstract:We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \…
  [2208.03787] Centralisers of finite groups in locally finite sim… Title:Centralisers of finite groups in locally finite simple groups Abstract:We answer in the negative a question of Hartley about representations of fin…
  [1311.6733] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1311.6733v1] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1311.6733v2] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1710.07183] Algorithms determining finite simple images of fini… Abstract:We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary …
  [1608.00461] Chabauty limits of simple groups acting on trees Title:Chabauty limits of simple groups acting on trees Abstract:Let $T$ be a locally finite tree without vertices of degree $1$. We show that among the c…
  [1710.07183v1] Algorithms determining finite simple images of fi… Abstract:We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary …
  [2210.14689] Non-abelian simple groups which occur as the type o… Abstract: We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of…
  [1608.00461v2] Chabauty limits of simple groups acting on trees Title:Chabauty limits of simple groups acting on trees Abstract:Let T be a locally finite tree without vertices of degree 1. We show that among closed su…
  [1608.00461v1] Chabauty limits of simple groups acting on trees Title:Chabauty limits of simple groups acting on trees Abstract:Let T be a locally finite tree without vertices of degree 1. We show that among closed su…
  [1608.00461v3] Chabauty limits of simple groups acting on trees Title:Chabauty limits of simple groups acting on trees Abstract:Let $T$ be a locally finite tree without vertices of degree $1$. We show that among the c…
  [2210.09635] The spread of finite and infinite groups Title:The spread of finite and infinite groups Abstract:It is well known that every finite simple group has a generating pair. Moreover, Guralnick and Ka…
  [1009.6183] Simple groups admit Beauville structures Abstract: We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit…
  [1107.4130] Frobenius' result on simple groups of order (p^3-p)/2 Title:Frobenius' result on simple groups of order (p^3-p)/2 Abstract:The complete list of pairs of non-isomorphic finite simple groups having the same or…
  [2105.03614] Simple groups with Brauer trees of principal blocks… Title:Simple groups with Brauer trees of principal blocks in the shape of a star Abstract:We have found a list of finite simple groups with cyclic Sylow …
  [1009.6183v1] Simple groups admit Beauville structures Title:Simple groups admit Beauville structures Abstract:We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups oth…
  [2210.14689v2] Non-abelian simple groups which occur as the type… Title:Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension Abstract:We determine the finite non-abelian s…
  [2210.14689v1] Non-abelian simple groups which occur as the type… Title:Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension Abstract:We determine the finite non-abelian s…
  [1112.3739] Groups of Finite Morley Rank with a Pseudoreflection… Title:Groups of Finite Morley Rank with a Pseudoreflection Action Abstract:In this work, we give two characterisations of the general linear group as a g…
  [1511.08241] Simple groups of dynamical origin Title:Simple groups of dynamical origin Abstract:We associate with every etale groupoid G two normal subgroups S(G) and A(G) of the topological full grou…
  [1802.09258] Simple groups of birational transformations in dime… Title:Simple groups of birational transformations in dimension two Abstract:We classify simple groups that act by birational transformations on compact c…
  [1312.2311] Simple groups of automorphisms of trees determined b… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [2204.00775] Class Numbers, Cyclic Simple Groups and Arithmetic Title:Class Numbers, Cyclic Simple Groups and Arithmetic Abstract:Here we initiate a program to study relationships between finite groups and arithmetic-…
  [1802.05222] Groups of finite Morley rank with a generically sha… Abstract:We prove that if $G$ is a group of finite Morley rank which acts definably and generically sharply $n$-transitively on a connected abelian group…
  [2107.09997] Groups of finite Morley rank with a generically mul… Abstract:We investigate the configuration where a group of finite Morley rank acts definably and generically $m$-transitively on an elementary abelian $p…
  [0706.0790] Free Actions of Finite Groups on $S^n \times S^n$ Title:Free Actions of Finite Groups on $S^n \times S^n$ Abstract: Let $p$ be an odd prime. We construct a non-abelian extension $\Gamma$ of $S^1$ by $Z/p…
  Actions of large finite groups on aspherical manifolds Abstract. In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism grou…
  [1312.2311v1] Simple groups of automorphisms of trees determined… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [1312.2311v2] Simple groups of automorphisms of trees determined… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [math/0511191] Orders of Finite Groups of Matrices Title:Orders of Finite Groups of Matrices Abstract: We present a new proof of a theorem of Schur's determining the least common multiple of the orders of…
  [0809.0074] Group algebras of finite groups as Lie algebras Title:Group algebras of finite groups as Lie algebras Abstract: We consider the natural Lie algebra structure on the (associative) group algebra of a fin…
  [1712.04553] MaxDim of some simple groups Title:MaxDim of some simple groups Abstract:MaxDim, along with it relatives m and i, are group invariants analogous to the concept of dimension in vector…
  [1209.2484] On the number of finite subgroups of a lattice Title:On the number of finite subgroups of a lattice Abstract:We show that the number of conjugacy classes of maximal finite subgroups of a lattice in a …
  [1712.04553v1] MaxDim of some simple groups Title:MaxDim of some simple groups Abstract:MaxDim, along with it relatives m and i, are group invariants analogous to the concept of dimension in vector…
  [2402.02269] The binary actions of simple groups with a single c… Title:The binary actions of simple groups with a single conjugacy class of involutions Abstract:We continue our investigation of binary actions of simple…
  [1102.3021] Spectra of finite symplectic and orthogonal groups Title:Spectra of finite symplectic and orthogonal groups Abstract:The spectra of a finite group is the set of its element orders. We obtain an arithmetic…
  [2307.00403] Amenability of finite energy path and loop groups Title:Amenability of finite energy path and loop groups Abstract:It is shown that the groups of finite energy (that is, Sobolev class $H^1$) paths and lo…
  [2012.08400] Constructing finite simple solutions of the Yang-Ba… Abstract:We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case wher…
  [1102.3021v1] Spectra of finite symplectic and orthogonal groups Title:Spectra of finite symplectic and orthogonal groups Abstract:The spectra of a finite group is the set of its element orders. We obtain an arithmetic…
  [1703.07905] A finite simple group is CCA if and only if it has … Title:A finite simple group is CCA if and only if it has no element of order four Abstract:A Cayley graph for a group $G$ is CCA if every automorphism of…
  [1807.03879] Expansion in simple groups Title:Expansion in simple groups Abstract:Two short seminal papers of Margulis used Kazhdan's property $(T)$ to give, on the one hand, explicit construct…
  [2008.02558] Shintani descent, simple groups and spread Title:Shintani descent, simple groups and spread Abstract:The spread of a group $G$, written $s(G)$, is the largest $k$ such that for any nontrivial elem…
  [1410.6111] On homology of finite topological spaces Title:On homology of finite topological spaces Abstract:We develop a new method to compute the homology groups of finite topological spaces (or equivalen…

• http://mathoverflow.net/a/70645 — found via Mwmbl

  gr.group theory - Number of finite simple groups of given order …

  $\begingroup$Here's a pedantic comment: my understanding (which might be wrong!) was that the final flourish of the classification was a computation whic…

  gr.group theory - maximal subgroups of finite simple groups - Ma… 2 Answers 2 Prop: If $G$ is a finite simple group, then a maximal subgroup of $G$ is trivial or has composite order Proof: A maximal subgroup of $G$ bein…
  gr.group theory - Heuristic argument that finite simple groups _… Obviously there exists a list of the finite simple groups, but why should it be a nice list, one that you can write down? Solomon's AMS article goes some …
  gr.group theory - Generating finite simple groups with $2$ eleme… 6 Answers 6 The answer to your question is yes. Moreover, if you pick two random elements from a finite simple group, then they generate the whole group …
  finite groups - Applications of fusion systems - MathOverflow What are the applications of theory of fusion systems to finite group theory or representation theory of finite groups? More concretely, is there any imp…
  finite groups - Measures of non-abelian-ness - MathOverflow Let $G$ be a finite non-abelian group of $n$ elements. I would like a measure that intuitively captures the extent to which $G$ is non-commutative. One e…

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  Finite non-abelian simple groups - Pastebin.com

• https://terrytao.wordpress.com/tag/finite-simple-groups/ — found via Mwmbl

  finite simple groups | What's new

  Emmanuel Breuillard, Ben Green, Bob Guralnick, and I have just uploaded to the arXiv our joint paper “Expansion in finite simple groups of Lie type“. Thi…

• http://www.youtube.com/watch?gl=GB&hl=en-GB&v=BipvGD-LCjU — found via Mwmbl

  Finite Simple Group (of Order Two) - YouTube