Projective metabelian nonfree groups

Publisher： Cambridge University Press

E-ISSN： 1755-1633|13|1|101-115

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.13, Iss.1, 1975-08, pp. : 101-115

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Abstract

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.

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