Lower bounds for the number of conjugacy classes of finite groups

In 2000, L. Héthelyi and B. Külshammer proved that if p is a prime number dividing the order of a finite solvable group G, then G has at least $2\sqrt{p-1}$ conjugacy classes. In this paper we show that if p is large, the result remains true for arbitrary finite groups.

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2009-11, Vol.147 (3), p.567-577
Main Author: KELLER, THOMAS MICHAEL
Format: Article
Language:English
Subjects:
Mathematics
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Summary:In 2000, L. Héthelyi and B. Külshammer proved that if p is a prime number dividing the order of a finite solvable group G, then G has at least $2\sqrt{p-1}$ conjugacy classes. In this paper we show that if p is large, the result remains true for arbitrary finite groups.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004109990090