A residual property of certain linear groups

Stebe, Peter F.

doi:10.1090/S0002-9947-1987-0887513-1

A residual property of certain linear groups
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by Peter F. Stebe

Trans. Amer. Math. Soc. 302 (1987), 333-340

DOI: https://doi.org/10.1090/S0002-9947-1987-0887513-1

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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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On infinite soluble groups

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On infinite soluble groups

44

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