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The notion of a Crawley p-group is well known in Abelian group theory. In this present work, a corresponding concept is introduced for torsion-free groups. The principal result, which uses the set-theoretic notions of the diamond and Martin’s axiom, establishes an independence result for N1-free Crawley groups.
Brendan Goldsmith ,Corner, A.L.S. and R. Gobel: On torsion-free Crawley groups. Quarterly Journal of Mathmatics, Oxford, 2, 57, 2006, pp.183-192.