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Varieties and finite groups

Published online by Cambridge University Press:  09 April 2009

L. G. Kovács
L. G. Kovács
Affiliation:
Australian National UniversityCanberra
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The theory of discrete, abstract groups, as presented in current texts, consists of investigations of various special classes of groups: it has very few completely general results. For some classes (say, for finite groups) the investigations have been extensive and successful; in a few cases (say, for finitely generated abelian groups) they have even reached a sense of completeness. The choice of some of these classes was dictated by the needs of other branches of mathematics. Many more were introduced with the view of extending the scope of certain powerful but special results, and a large part of the literature is taken up by elaborate counterexamples which mark the limits of these generalizations. In so far as one is looking for some kind of classification theory, it is immediately evident that the classes investigated were chosen by historical accident rather than by any master plan, and so far do not appear to form the initial part of a pattern which could be enlarged and completed in the future.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 5 - 19
Copyright
Copyright © Australian Mathematical Society 1969

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