On finitely generated profinite groups II, products in quasisimple groups
| dc.creator | Nikolov, Nikolay | |
| dc.creator | Segal, Dan | |
| dc.date | 2006-04-18 | |
| dc.date.accessioned | 2026-07-07T07:11:03Z | |
| dc.date.available | 2026-07-07T07:11:03Z | |
| dc.description | 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 $| S/\mathrm{Z}(S)| >C$, $β_{j}$ $ (j=1,...,M)$ are any automorphisms of $S$, and $q_{j}$ $ (j=1,...,M)$ are any divisors of $q$, then there exist inner automorphisms $α_{j}$ of $S$ such that $S=\prod_{1}^{M}[S,(α_{j}β_{j})^{q_{j}}]$. These results, which rely on the Classification of finite simple groups, are needed to complete the proofs of the main theorems of Part I. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604400 | |
| dc.identifier | http://arxiv.org/abs/math/0604400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111612 | |
| dc.subject | Group Theory | |
| dc.subject | 20F69; 20D05 | |
| dc.title | On finitely generated profinite groups II, products in quasisimple groups | |
| dc.type | text |