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SOME PROPERTIES OF SEMI-ABELIAN $p$-GROUPS

Part of: Representation theory of groups Connections with homological algebra and category theory

Published online by Cambridge University Press:  15 October 2014

MOHAMMED T. BENMOUSSA  and
YASSINE GUERBOUSSA
MOHAMMED T. BENMOUSSA
Affiliation:
Department of Mathematics, University Kasdi Merbah Ouargla, Ouargla, Algeria email benmoussageo@gmail.com
YASSINE GUERBOUSSA*
Affiliation:
Department of Mathematics, University Kasdi Merbah Ouargla, Ouargla, Algeria email yassine_guer@hotmail.fr
*
✉yassine_guer@hotmail.fr
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Abstract

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We prove a cohomological property for a class of finite $p$-groups introduced earlier by Xu, which we call semi-abelian $p$-groups. This result implies that a semi-abelian $p$-group has noninner automorphisms of order $p$, which settles a long-standing problem for this class. We answer also, independetly, an old question posed by Xu about the power structure of semi-abelian $p$-groups.

Keywords

finite p-groupscohomology of groupsautomorphisms

MSC classification

Primary: 20D15: Nilpotent groups, $p$-groups
Secondary: 20J06: Cohomology of groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 86 - 91
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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