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Transversals in non-discrete groups

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Abstract

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroupS with a Tychonoff topologyT, it is proved that there exists a Hausdorff topological group in whichS 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, o) is such thatT S =T S is a locally compact Hausdorff topology onS, thenS 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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Authors and Affiliations

  1. Department of Mathematics, University of Allahabad, 211 002, Allahabad, India

    Ramji Lal & R. P. Shukla

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  1. Ramji Lal
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  2. R. P. Shukla
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Correspondence to Ramji Lal.

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Lal, R., Shukla, R.P. Transversals in non-discrete groups. Proc. Indian Acad. Sci. (Math. Sci.) 115, 429–435 (2005). https://doi.org/10.1007/BF02829804

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  • DOI: https://doi.org/10.1007/BF02829804

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