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On the Schur-Baer property

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Mohammad Reza R. Moghaddam
Mohammad Reza R. Moghaddam
Affiliation:
Department of Mathematics, Faculty of Science, University of Mashhad, Mashhad, Iran
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Abstract

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In 1957 P. Hall conjectured that every (finitely based) variety has the property that, for every group G, if the marginal factor-group is finite, then the verbal subgroup is also finite. The content of this paper is to present a precise bound for the order of the verbal subgroup of a G when the marginal factor-group is of order Pn (p a prime and n > 1) with respect to the variety of polynilpotent groups of a given class row. We also construct an example to show that the bound is attained and furthermore, we obtain a bound for the order of the Baer-invariant of a finite p-group with respect to the variety of polynilpotent groups.

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups 20F12: Commutator calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 343 - 361
Copyright
Copyright © Australian Mathematical Society 1981

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