Non-metacyclic groups acting with nilpotent centralizers

2023/05/11 by Emerson de Melo, de Melo, Emerson, Jhone Caldeira +1
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2305.07177

Abstract

Let A be a non-metacyclic finite group. Suppose that A acts coprimely on a finite group G in such a manner that C_G(a) is nilpotent for any a∈ A^#. In the present paper we investigate some conditions on A which imply that G is nilpotent with ``bounded'' nilpotency class. More precisely, we generalize known results on action of q-groups and Frobenius groups, where q is a prime.

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