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A NOTE ON AUTOMORPHISMS OF FINITE p-GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  30 March 2012

S. MOHSEN GHORAISHI
S. MOHSEN GHORAISHI*
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran (email: m.ghoraishi@sci.ui.ac.ir)
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Abstract

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Let p be an odd prime and let G be a finite p-group such that xZ(G)⊆xG, for all x∈G∖Z(G), where xG denotes the conjugacy class of x in G. Then G has a noninner automorphism of order p leaving the Frattini subgroup Φ(G) elementwise fixed.

Keywords

finite p-groupsautomorphisms of p-groupsnoninner automorphismsCamina pairs

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 24 - 26
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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