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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A residual property of certain linear groups

Author: Peter F. Stebe
Journal: Trans. Amer. Math. Soc. 302 (1987), 333-340
MSC: Primary 20E26; Secondary 20F10
MathSciNet review: 887513
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Abstract: An extension of residual finiteness, residual finiteness with respect to nests, is demonstrated for certain subgroups of $ GL(n,Z)$, the polycyclic by finite groups. It is also shown that groups containing a free subgroup of rank greater than $ 1$ cannot have the property. It is not settled whether or not there are other solvable by finite groups, subgroups allowed by Tits' theorem, that are residually finite with respect to nests.

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Keywords: Residual property, linear group, decision problem
Article copyright: © Copyright 1987 American Mathematical Society