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  • Author: Peter A. Linnell x
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Let G be a group of the form , the free product of n subgroups, and let M be a ℤG-module of the form . We shall give formulae in various situations for dℤG(M), the minimum number of elements required to generate M. In particular if C 1, C 2 are non-trivial finite cyclic groups of coprime orders, and F/RG is the free presentation obtained from the natural free presentations of the two factors, then the number of generators of the relation module, dℤG(R/R′), is 3. It seems plausible that the minimum number of relators of G should be 4, and this would give a finitely presented group with positive relation gap. However we cannot prove this last statement.