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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1285998
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1285998-2
PII: S 0002-9939(1995)1285998-2
Article copyright: © Copyright 1995 American Mathematical Society