Finite Group Theory

By Alexander Lubotzky, D. Segal. 2003

1,074 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/46db91e316941215d20ea66eb876aabf298a10aa

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Citations in the corpus

Thompson-like characterizations of the solvable radical ✩ (2006, neutral): “See [1] for the basic definitions and results.”
Generators and commutators in finite groups; abstract quotients of compact groups (2011, background): “Now let F ∗ = F(G0) denote the generalized Fitting subgroup of G0 (see [As], Section 31).”
The commuting graph of a soluble group (2012, background): “Our group theoretic notation is mostly standard and follows that in [1, 3].”
The classification of torsion endo-trivial modules (2005, background): “Alternatively, this appears explicitly in Exercise 5 of Chapter 8 of [As].”
Representation Theory of Finite Reductive Groups: Frontmatter (2004, methodology): “The axiomatic setup of BN-pairs (see [Asch86] §43, [Bour68] §IV, [CuRe87] §65) has been devised to cover the so-called Chevalley groups and check their simplicity.”
Product decompositions of quasirandom groups and a Jordan type theorem (2007, background): “normal quasisimple subgroups. The subgroup E = E(G) is generated by the components of G. The components of E(G) are exactly the components C j of G and Aut(E) permutes the components among themselves [As]. Denote the orbits of Aut(E) on the components by B k (k = 1,2,...). Then B k consists of t k i”
The admissibility of sporadic simple groups (2009, neutral): “In a recent paper, Wilcox [16] improved on Aschbacher’s results by proving that any minimal counterexample to the Hall–Paige conjecture must be a simple group.”
The structure of extra loops (2004, background): “Also |P ∩O(G)| = p, since P ∩O(G) ∈ Sylp(O (G)) ([1], (6.”
The motive of a classifying space (2014, background): “By definition of a triangulated category (such as DM(k;R)), every morphism X → Y fits into an exact triangle X → Y → Z → X[1].”