Geodesic
Tychonoff property for linear groups
Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 269-279

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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. 
@article{MZM_1998_63_2_a10,
     author = {A. N. Starkov},
     title = {Tychonoff property for linear groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {269--279},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a10/}
}
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A. N. Starkov. Tychonoff property for linear groups. Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a10/