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CONJUGACY CLASS SIZES OF CERTAIN DIRECT PRODUCTS

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

Published online by Cambridge University Press:  27 February 2012

CARLO CASOLO  and
ELISA MARIA TOMBARI
CARLO CASOLO*
Affiliation:
Dipartimento di Matematica ‘Ulisse Dini’, Università di Firenze, I-50134 Firenze, Italy (email: casolo@math.unifi.it)
ELISA MARIA TOMBARI
Affiliation:
Dipartimento di Matematica ‘Ulisse Dini’, Università di Firenze, I-50134 Firenze, Italy
*
✉For correspondence; e-mail: casolo@math.unifi.it
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Abstract

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We consider finite groups in which, for all primes p, the p-part of the length of any conjugacy class is trivial or fixed. We obtain a full description in the case in which for each prime divisor p of the order of the group there exists a noncentral conjugacy class of p-power size.

Keywords

finite groupsconjugacy classesdirect products

MSC classification

Secondary: 20E45: Conjugacy classes 20D60: Arithmetic and combinatorial problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 2 , April 2012 , pp. 217 - 231
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

The authors were partially supported by MIUR project ‘Teoria dei gruppi e applicazioni’.

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