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On soluble groups of prime-power exponent

Published online by Cambridge University Press:  17 April 2009

Warren Brisley  and
L.G. Kovács
Warren Brisley
Affiliation:
University of Newcastle, Newcastle, New South Wales
L.G. Kovács
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Let p be a prime and the variety of elementary abelian by elementary abelian p-groups. A result of Brisley and Macdonald is generalized as follows. If H is a finite group in and G is a soluble group of p–power exponent such that no section of G is isomorphic to H, then G is nilpotent and its class is bounded by a function of three variables: H, the exponent of G, and the soluble length of G. It is a corollary that if the variety generated by a soluble group G of finite exponent contains , then each finite group in is isomorphic to some section of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 389 - 396
Copyright
Copyright © Australian Mathematical Society 1971

References

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