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Metanilpotent varieties of groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

R. M. Bryant  and
A. N. Krasil'nikov
R. M. Bryant
Affiliation:
UMIST, PO Box 88, Manchester M60 1QD, UK e-mail: [email protected]
A. N. Krasil'nikov
Affiliation:
Moscow Pedagogical State University, 14 Krasnoprudnaya ul., Moscow 107140, Russia
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Abstract

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For each positive integer n let N2, n denote the variety of all groups which are nilpotent of class at most 2 and which have exponent dividing n. For positive integers m and n, let N2, mN2, n denote the variety of all groups which have a normal subgroup in N2, m with factor group in N2, n. It is shown that if G ∈N2, mN2, n, where m and n are coprime, then G has a finite basis for its identities.

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 55 - 84
Copyright
Copyright © Australian Mathematical Society 2002

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