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Original Articles

The group of automorphisms of an elementary-abelian-over-cyclic regular wreath product p-group

Pages 523-540 | Received 17 Nov 2017, Accepted 11 May 2018, Published online: 04 Apr 2019
 

Abstract

Let W denote the regular wreath product finite group CE where C is a cyclic p-group and E is an elementary abelian p-group. Let A denote the subgroup of Aut(W) consisting of those automorphisms that act trivially on W/B, where B is the base group. We determine A by describing where each of its elements map a certain generating set for W. We find that A is as large as possible in a certain sense. We determine some information about the subgroup structure of A, and we prove that every class-preserving automorphism of W is an inner automorphism of W.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

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