Weak maximality condition and polycyclic groups

Authors:
Y. K. Kim and A. H. Rhemtulla

Journal:
Proc. Amer. Math. Soc. **123** (1995), 711-714

MSC:
Primary 20F16; Secondary 06F15, 20E26, 20F60

DOI:
https://doi.org/10.1090/S0002-9939-1995-1285998-2

MathSciNet review:
1285998

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Abstract: A group *G* is called strongly restrained if there exists an integer *n* such that 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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DOI:
https://doi.org/10.1090/S0002-9939-1995-1285998-2

Article copyright:
© Copyright 1995
American Mathematical Society