Vol. 7, No. 2, 2014

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
On groups with a class-preserving outer automorphism

Peter A. Brooksbank and Matthew S. Mizuhara

Vol. 7 (2014), No. 2, 171–179
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.

Keywords
$p$-groups, class-preserving automorphisms, polycyclic groups
Mathematical Subject Classification 2010
Primary: 20D15, 20D45, 20E45
Milestones
Received: 4 August 2012
Revised: 7 November 2012
Accepted: 17 November 2012
Published: 16 November 2013

Communicated by Nigel Boston
Authors
Peter A. Brooksbank
Department of Mathematics
Bucknell University
380 Olin Science Building
Lewisburg, PA 17837
United States
Matthew S. Mizuhara
Department of Mathematics
Bucknell University
380 Olin Science Building
Lewisburg, PA 17837
United States