Vol. 7, No. 2, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
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