Publication Date

2014

Journal

Involve

Volume

7

Issue

2

First Page

171

Last Page

179

Abstract

Four infinite families of 2-groups are presented, all of whose members possess an outer automorphism that preserves conjugacy classes. The groups in these families are central extensions of their predecessors by a cyclic group of order 2. For each integer r>1, there is precisely one 2-group of nilpotency class r in each of the four families. All other known families of 2-groups possessing a class-preserving outer automorphism consist entirely of groups of nilpotency class 2.

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Algebra Commons

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