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ON FINITE p-GROUPS WITH SUBGROUPS OF BREADTH 1

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

Published online by Cambridge University Press:  12 April 2010

GIOVANNI CUTOLO ,
HOWARD SMITH  and
JAMES WIEGOLD
GIOVANNI CUTOLO*
Affiliation:
Università degli Studi di Napoli ‘Federico II’, Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Via Cintia—Monte S. Angelo, I-80126 Napoli, Italy (email: cutolo@unina.it)
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA (email: howsmith@bucknell.edu)
JAMES WIEGOLD
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4Y, UK
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Abstract

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We consider finite p-groups G in which every cyclic subgroup has at most p conjugates. We show that the derived subgroup of such a group has order at most p2. Further, if the stronger condition holds that all subgroups have at most p conjugates then the central factor group has order p4 at most.

Keywords

finite p-groupsconjugacy classesbreadth

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 20E45: Conjugacy classes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 84 - 98
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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