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On varieties of metabelian p-groups, and their laws

Published online by Cambridge University Press:  09 April 2009

Warren Brisley
Warren Brisley
Affiliation:
Department of Mathematics University of Newcastle
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The purpose of this article is to present some results on varieties of metabelian p-groups, nilpotent of class c, with the prime p greater than c. After some preliminary lemmas in § 3, it is established in § 4, Theorem 3, that there is a simple basis for the laws of such a variety, and this basis is explicitly stated. This allows the description of the lattice of such varieties, and in § 5, Theorem 4, it is shown that each such variety has a two-generator member which generates it; this is established by the help of Theorem 5, which states that each critical group is a two-generator group, and Theorem 6, which gives explicitly the varieties generated by the proper subgroups, by the proper quotient groups, and by the proper factor groups of such a critical group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 64 - 80
Copyright
Copyright © Australian Mathematical Society 1967

References

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