Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Centralizers of coprime automorphisms of finite groups (1112.5880v1)

Published 26 Dec 2011 in math.GR

Abstract: Let $A$ be an elementary abelian group of order $p{k}$ with $k\geq 3$ acting on a finite $p'$-group $G$. The following results are proved. If $\gamma_{k-2}(C_{G}(a))$ is nilpotent of class at most $c$ for any $a\in A{#}$, then $\gamma_{k-2}(G)$ is nilpotent and has ${c,k,p}$-bounded nilpotency class. If, for some integer $d$ such that $2{d}+2\leq k$, the $d$th derived group of $C_{G}(a)$ is nilpotent of class at most $c$ for any $a\in A{#}$, then the $d$th derived group $G{(d)}$ is nilpotent and has ${c,k,p}$-bounded nilpotency class. Earlier this was known only in the case where $k\leq 4$.

Summary

We haven't generated a summary for this paper yet.