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Groups with large conjugacy classes
Published online by Cambridge University Press: 09 April 2009
Abstract
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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