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ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 September 2012

A. R. JAMALI  and
M. VISEH
A. R. JAMALI*
Affiliation:
Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, 599 Taleghani Ave., Tehran 15618, Iran (email: jamali@tmu.ac.ir)
M. VISEH
Affiliation:
Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, 599 Taleghani Ave., Tehran 15618, Iran (email: m.viseh@tmu.ac.ir)
*
✉For correspondence; e-mail: jamali@tmu.ac.ir
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Abstract

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In this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Φ(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.

Keywords

finite p-groupsnoninner automorphismpowerful p-groupscyclic commutator subgroup

MSC classification

Secondary: 20D45: Automorphisms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 278 - 287
Copyright
©2012 Australian Mathematical Publishing Association Inc.

References

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