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Projective metabelian nonfree groups

Published online by Cambridge University Press:  17 April 2009

V.A. Artamonov
V.A. Artamonov
Affiliation:
Department of Mechanics and Mathematics, Moscow State University, Moscow, USSR; Department of Mathematics, Bedford College, University of London, London, England.
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Abstract

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This paper is concerned with projective metabelian -groups. where is the variety of all abelian groups, - of all abelian groups of exponent n. Let P be a projective -group. Since the group P/P′ is a free abelian group. Define rank P = rank P/P′. It is shown that for all numbers r, n > 1, except r = n = 2, there exists a protective nonfree -group of rank r with r + 1 generators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 101 - 115
Copyright
Copyright © Australian Mathematical Society 1975

References

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