The Frattini subgroup of a Lie group and the topological rank of a Lie group Full article
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Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2024, Volume: 640, Pages: 326-367 Pages count : 42 DOI: 10.1016/j.jalgebra.2023.10.026 | ||||
| Tags | Frattini subgroup of a Lie group, number of topological generators of a Lie group, number of generators of a Lie algebra | ||||
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Abstract:
We define the Frattini subgroup of a topological group G as the set of non-generators. We describe it completely for connected Lie groups, first for the case that G is solvable and then in general. As an application we determine the topological rank of G, that is the minimal number of elements needed to generate a dense subgroup of G.
Cite:
Abels H.
, Noskov G.A.
The Frattini subgroup of a Lie group and the topological rank of a Lie group
Journal of Algebra. 2024. V.640. P.326-367. DOI: 10.1016/j.jalgebra.2023.10.026 WOS Scopus РИНЦ OpenAlex
The Frattini subgroup of a Lie group and the topological rank of a Lie group
Journal of Algebra. 2024. V.640. P.326-367. DOI: 10.1016/j.jalgebra.2023.10.026 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 28, 2022 |
| Published online: | Nov 14, 2023 |
| Published print: | Feb 15, 2024 |
Identifiers:
| Web of science: | WOS:001125402500001 |
| Scopus: | 2-s2.0-85177827164 |
| Elibrary: | 64894589 |
| OpenAlex: | W4388672865 |
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