2006/04/18 by Nikolay Nikolov, Nikolov, Nikolay, Dan Segal +1 · 1 citation
Computer Science · Mathematics · #20D05 #20F69 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20D05 #msc:20F69
paper · pdf · doi:10.48550/arxiv.math/0604400
34 pages
arxiv created 2006/04/18 · openalex publication_date 2006/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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=∏1M[S,(αjβj)^qj]. These results, which rely on the Classification of finite simple groups, are needed to complete the proofs of the main theorems of Part I.