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On groups with a
class-preserving outer automorphism
Peter A. Brooksbank and Matthew S. Mizuhara
Vol. 7 (2014), No. 2, 171–179
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Abstract |
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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 , there is precisely one 2-group of nilpotency class 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
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Mathematical Subject Classification 2010
Primary: 20D15, 20D45, 20E45
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Milestones
Received: 4 August 2012
Revised: 7 November 2012
Accepted: 17 November 2012
Published: 16 November 2013
Communicated by Nigel Boston
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Authors |
| Peter A. Brooksbank | |
| Department of Mathematics Bucknell University 380 Olin Science Building Lewisburg, PA 17837 United States |
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| Matthew S. Mizuhara | |
| Department of Mathematics Bucknell University 380 Olin Science Building Lewisburg, PA 17837 United States |
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