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Finite Groups with a given Number of Conjugate Classes

Published online by Cambridge University Press:  20 November 2018

John Poland
John Poland*
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, and Carleton University, Ottawa
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This paper presents a list of all finite groups having exactly six and seven conjugate classes and an outline of the background necessary for the proof, and gives, in particular, two results which may be of independent interest. In 1903 E. Landau (8) proved, by induction, that for each the equation

*

has only finitely many solutions over the positive integers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 456 - 464
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This material formed part of the author's dissertation, McGill University, May, 1966.

*

I thank my director H. Schwerdtfeger for calling my attention to Landau's theorem, from this reference.

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