Transversals in non-discrete groups

Details Transversals in non-discrete groups Transversals in non-discrete groups

2005-12-14

arxiv.org/abs/math/0512316v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 429-435

Mathematics

Group Theory

7 pages

Scientific paper

The concept of `topological right transversal' is introduced to study right transversals in topological groups. Given any right quasigroup $S$ with a Tychonoff topology $T$, it is proved that there exists a Hausdorff topological group in which $S$ can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological right transversal $(S, T_{S}, T^{S}, \circ)$ is such that $T_{S} = T^{S}$ is a locally compact Hausdorff topology on $S$, then $S$ can be embedded as a right transversal of a closed subgroup in a Hausdorff topological group which is universal in some sense.

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