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Mat. Zametki, 1998, Volume 63, Issue 2, Pages 269–279 (Mi mz1273)  

Tychonoff property for linear groups

A. N. Starkov

Russian Electrotechnical Institute Named after V. I. Lenin

Abstract: A criterion for a wide class of topological groups which includes linear discrete groups and Lie groups to be Tychonoff groups is established. The main result provides a criterion for an almost polycyclic group to have the Tychonoff property. By the well-known Tits alternative, this yields the required criterion for linear discrete groups. In conclusion it is pointed out that a particular case of the presented proof yields a Tychonoff property criterion for Lie groups. In addition, an example of a polycyclic group without Tychonoff subgroups of finite index is constructed.

DOI: https://doi.org/10.4213/mzm1273

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English version:
Mathematical Notes, 1998, 63:2, 233–241

Bibliographic databases:

UDC: 512.546
Received: 24.06.1996

Citation: A. N. Starkov, “Tychonoff property for linear groups”, Mat. Zametki, 63:2 (1998), 269–279; Math. Notes, 63:2 (1998), 233–241

Citation in format AMSBIB
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\paper Tychonoff property for linear groups
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\pages 269--279
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\jour Math. Notes
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\pages 233--241
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