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

Residual linearity for certain nilpotent groups


Author: P. Menal
Journal: Proc. Amer. Math. Soc. 68 (1978), 27-31
MSC: Primary 20E15
Addendum: Proc. Amer. Math. Soc. 77 (1979), 19-22.
MathSciNet review: 0460465
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Abstract: In this note we consider relations between residual finiteness and residual linearity for a nilpotent group G. We show, amongst other things, that if the center and the commutator subgroup of G are finitely generated and G is residually linear, then G is residually finite. Indeed the property which we use on linear groups is that linear groups satisfy the minimal condition on centralizers.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0460465-4
PII: S 0002-9939(1978)0460465-4
Keywords: Nilpotent group, residually finite, residually linear
Article copyright: © Copyright 1978 American Mathematical Society