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The Frattini subgroup of a Lie group and the topological rank of a Lie group Научная публикация

Журнал

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Вых. Данные

Год: 2024, Том: 640, Страницы: 326-367 Страниц : 42 DOI: 10.1016/j.jalgebra.2023.10.026

Ключевые слова

Frattini subgroup of a Lie group, number of topological generators of a Lie group, number of generators of a Lie algebra

Авторы

Abels H. ¹ , Noskov G.A. ²

Организации

1	Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2	The Sobolev Institute of Mathematics, Pevtsova 13, 644099 Omsk, Russia

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.

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

Поступила в редакцию:	28 дек. 2022 г.
Опубликована online:	14 нояб. 2023 г.
Опубликована в печати:	15 февр. 2024 г.

Web of science:	WOS:001125402500001
Scopus:	2-s2.0-85177827164
РИНЦ:	64894589
OpenAlex:	W4388672865

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