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ON FINITE p-GROUPS WITH SUBGROUPS OF BREADTH 1

Part of: Structure and classification of infinite or finite groups Representation theory of 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: [email protected])
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA (email: [email protected])
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

[1]Cutolo, G., Smith, H. and Wiegold, J., ‘The nilpotency class of p-groups in which subgroups have few conjugates’, J. Algebra 300(1) (2006), 160–170.CrossRefGoogle Scholar
[2]Knoche, H.-G., ‘Über den Frobenius’schen Klassenbegriff in nilpotenten Gruppen’, Math. Z. 55 (1951), 71–83.CrossRefGoogle Scholar
[3]Kraus, D., ‘Bounds concerning conjugacy in finite p-groups’, PhD Thesis, University of Wales College of Cardiff, 1995.Google Scholar
[4]Macdonald, I. D., ‘Some explicit bounds in groups with finite derived groups’, Proc. London Math. Soc. (3) 11 (1961), 23–56.CrossRefGoogle Scholar
[5]McKay, S., Finite p-groups, Queen Mary Maths Notes, 18 (University of London, Queen Mary, School of Mathematical Sciences, London, 2000).Google Scholar
[6]Robinson, D. J. S., A Course in the Theory of Groups, 2nd edn, Graduate Texts in Mathematics, 80 (Springer, New York, 1996).CrossRefGoogle Scholar