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Class preserving automorphisms of Blackburn groups

Part of: Rings and algebras arising under various constructions Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Allen Herman  and
Yuanlin Li
Allen Herman
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina Saskatchewan S4S 0A2, Canada, e-mail: aherman@math.uregina.ca
Yuanlin Li
Affiliation:
Department of Mathematics, Brock University, St. Catharine's, Ontario L2S 3A1, Canada, e-mail: yli@brocku.ca
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Abstract

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In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms.

MSC classification

Secondary: 20D45: Automorphisms 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 3 , June 2006 , pp. 351 - 358
Copyright
Copyright © Australian Mathematical Society 2006

References

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