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Groups with few conjugacy classes

Part of: Representation theory of groups

Published online by Cambridge University Press:  31 March 2011

László Héthelyi ,
Erzsébet Horváth ,
Thomas Michael Keller  and
Attila Maróti
László Héthelyi
Affiliation:
Department of Algebra, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3–9, 1521 Budapest, Hungary ([email protected]; [email protected])
Erzsébet Horváth
Affiliation:
Department of Algebra, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3–9, 1521 Budapest, Hungary ([email protected]; [email protected])
Thomas Michael Keller
Affiliation:
Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, USA ([email protected])
Attila Maróti
Affiliation:
MTA Alfréd Rényi Institute of Mathematics, Réaltanoda utca 13–15, 1053 Budapest, Hungary ([email protected])
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Abstract

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Let G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of conjugacy classes of G. By disregarding at most finitely many non-solvable p-solvable groups G, we have with equality if and only if if is an integer, and CG(Cp) = Cp. This extends earlier work of Héthelyi, Külshammer, Malle and Keller.

Keywords

finite groupconjugacy classeslower boundFrobenius group

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 423 - 430
Copyright
Copyright © Edinburgh Mathematical Society 2011

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