Abstract
The paper is devoted to the study of properties of a class of subgroups H in Lie groups G that was recently introduced by the author. A closed subgroup H in a Lie group G is said to be plesio-uniform if there is a closed subgroup P of G that contains H and for which P is uniform in G and H is quasi-uniform in P. In the paper we give answers to several natural questions concerning plesio-uniform subgroups. It is proved that one obtains the same notion of plesio-uniformity when transposing the conditions of uniformity and quasi-uniformity in the definition of plesio-uniformity of a subgroup. If a closed subgroup H of G contains a plesio-uniform subgroup, then H is also plesio-uniform. Other properties of plesio-uniform subgroups are also considered.
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Gorbatsevich, V.V. On the Properties of Plesio-Uniform Subgroups in Lie Groups. Mathematical Notes 69, 306–312 (2001). https://doi.org/10.1023/A:1010223222690
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DOI: https://doi.org/10.1023/A:1010223222690