On finitely generated profinite groups, II: products in quasisimple groups

By Nikolay Nikolov, D. Segal. 2006

85 citations recorded by the source corpus.

We prove two results. (1) There is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D ‘twisted commutators’ defined by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M = M(q) such that: if S is a finite quasisimple group with |S/Z(S)| >C , βj (j =1 ,... , M) are any automorphisms of S, and qj (j =1 ,... , M) are any divisors of q, then there exist inner automorphisms αj of S such that S = � M [S, (αjβj) q j ]. These results, which rely on the classification of finite simple groups, are needed to complete the proofs of the main theorems of Part I.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2b194384663ae7ec4f6b70a9271c4f6cd0fc23b5

Citations in the corpus

• Characters of symmetric groups: sharp bounds and applications (2008, unknown): “See Borel [Bo] for algebraic groups, Nikolov and Segal [NS1], [ NS2 ] for profinite groups, as well as [LiSh1], [DPSSh], [L], [Sh] and [LaSh].”