The Frattini subgroup of a Lie group and the topological rank of a Lie group
Abels H, Noskov GA (2024)
Journal of Algebra 640: 326-367.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Abels, HerbertUniBi;
Noskov, G. A.
Einrichtung
Abstract / Bemerkung
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.(c) 2023 Elsevier Inc. All rights reserved.
Stichworte
Frattini subgroup of a Lie group;
Number of topological generators of a;
Lie group;
Number of generators of a Lie algebra
Erscheinungsjahr
2024
Zeitschriftentitel
Journal of Algebra
Band
640
Seite(n)
326-367
ISSN
0021-8693
eISSN
1090-266X
Page URI
https://pub.uni-bielefeld.de/record/2985887
Zitieren
Abels H, Noskov GA. The Frattini subgroup of a Lie group and the topological rank of a Lie group. Journal of Algebra. 2024;640:326-367.
Abels, H., & Noskov, G. A. (2024). The Frattini subgroup of a Lie group and the topological rank of a Lie group. Journal of Algebra, 640, 326-367. https://doi.org/10.1016/j.jalgebra.2023.10.026
Abels, Herbert, and Noskov, G. A. 2024. “The Frattini subgroup of a Lie group and the topological rank of a Lie group”. Journal of Algebra 640: 326-367.
Abels, H., and Noskov, G. A. (2024). The Frattini subgroup of a Lie group and the topological rank of a Lie group. Journal of Algebra 640, 326-367.
Abels, H., & Noskov, G.A., 2024. The Frattini subgroup of a Lie group and the topological rank of a Lie group. Journal of Algebra, 640, p 326-367.
H. Abels and G.A. Noskov, “The Frattini subgroup of a Lie group and the topological rank of a Lie group”, Journal of Algebra, vol. 640, 2024, pp. 326-367.
Abels, H., Noskov, G.A.: The Frattini subgroup of a Lie group and the topological rank of a Lie group. Journal of Algebra. 640, 326-367 (2024).
Abels, Herbert, and Noskov, G. A. “The Frattini subgroup of a Lie group and the topological rank of a Lie group”. Journal of Algebra 640 (2024): 326-367.
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