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Varieties and simple groups

Published online by Cambridge University Press:  09 April 2009

Gareth A. Jones
Gareth A. Jones
Affiliation:
Department of Mathematics, University of Southampton, England
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In her book on varieties of groups, Hanna Neumann posed the following problem [13, p. 166]: “

Can a variety other than D contain an infinite number of non-isomorphic non-abelian finite simple groups?”

The answer to this question does not seem to be known at present. However, in [7], Heineken and Neumann described an algorithm for determining whether or not there are any non-abelian finite simple groups satisfying a given law. They also outlined a way in which their algorithm could be used to show that “only finitely many of the known non-abelian finite simple groups can satisfy a given non-trivial law”; in this paper, we shall follow their suggestions, and prove the

THEOREM. Let g be a set of mutually non-isomorphic non-abelian finite simple groups, each of which is either an alternating group or a group of Lie type, and let g generate a proper subvariety of D. Then y is finite.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 2 , March 1974 , pp. 163 - 173
Copyright
Copyright © Australian Mathematical Society 1974

References

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