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SOME PROPERTIES OF SEMI-ABELIAN $p$-GROUPS

Published online by Cambridge University Press:  15 October 2014

MOHAMMED T. BENMOUSSA
Affiliation:
Department of Mathematics, University Kasdi Merbah Ouargla, Ouargla, Algeria email [email protected]
YASSINE GUERBOUSSA*
Affiliation:
Department of Mathematics, University Kasdi Merbah Ouargla, Ouargla, Algeria email [email protected]
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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.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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