Finite groups and the fixed points of coprime automorphisms

Shumyatsky, Pavel

doi:10.1090/S0002-9939-01-06125-1

Finite groups and the fixed points of coprime automorphisms
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Proc. Amer. Math. Soc. 129 (2001), 3479-3484 Request permission

Abstract:

Let $p$ be a prime, and let $G$ be a finite $p’$-group acted on by an elementary abelian $p$-group $A$. The following results are proved: 1. If $|A|\ge p^3$ and $C_G(a)$ is nilpotent of class at most $c$ for any $a\in A^\#$, then the group $G$ is nilpotent of $\{c,p\}$-bounded class. 2. If $|A|\ge p^4$ and $C_G(a)’$ is nilpotent of class at most $c$ for any $a\in A^\#$, then the derived group $G’$ is nilpotent of $\{c,p\}$-bounded class.

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