Weak maximality condition and polycyclic groups

Kim, Y. K.; Rhemtulla, A. H.

doi:10.1090/S0002-9939-1995-1285998-2

Weak maximality condition and polycyclic groups
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by Y. K. Kim and A. H. Rhemtulla PDF

Proc. Amer. Math. Soc. 123 (1995), 711-714 Request permission

Abstract:

A group G is called strongly restrained if there exists an integer n such that $\langle {x^{(y)}}\rangle$ can be generated by n elements for all x, y in G. We show that a group G is polycyclic-by-finite if and only if G is a finitely generated strongly restrained group in which every nontrivial finitely generated subgroup has a nontrivial finite quotient. This provides a general setting for various results in soluble and residually finite groups that have appeared recently.

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