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ON NONINNER 2-AUTOMORPHISMS OF FINITE 2-GROUPS

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  29 May 2014

ALIREZA ABDOLLAHI  and
S. MOHSEN GHORAISHI
ALIREZA ABDOLLAHI
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran email a.abdollahi@math.ui.ac.ir
S. MOHSEN GHORAISHI*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Chamran University, Ahvaz, Iran email m.ghoraishi@scu.ac.ir
*
✉m.ghoraishi@scu.ac.ir
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Abstract

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Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ be a finite 2-group. If $G$ is of coclass 2 or $(G,Z(G))$ is a Camina pair, then $G$ admits a noninner automorphism of order 2 or 4 leaving the Frattini subgroup elementwise fixed.

Keywords

finite p-groupnoninner automorphismcoclassCamina pair

MSC classification

Secondary: 20D45: Automorphisms 20E36: Automorphisms of infinite groups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 227 - 231
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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