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Groups with large conjugacy classes

Published online by Cambridge University Press:  09 April 2009

Bola O. Balogun
Bola O. Balogun
Affiliation:
Department of Mathematics, University of Ife, ILE-IFE, Nigeria.
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Abstract

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A finite group is called repetition-free if its conjugacy classes have distinct sizes. It is known that a supersolvable repetition-free group is necessarily isomorphie to Sym(3). the symmetric group on three symbols. Thus the question arises as to whether Sym (3) is the only repetition-free group. In this paper it is proved that if mk denotes the minimum of the orders of the centralizers of elements of a repetition-free group G and mk ≦ 4 then G is isomorphie to Sym (3).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 257 - 265
Copyright
Copyright © Australian Mathematical Society 1977

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