Solvable groups with a given solvable length, and minimal composition length

Abstract We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we show that {2n+1} is the sharpest upper bound for the derived length of solvable subgroups of the group {\mathrm{Diff}({\mathbb{C}}^{n},0)} of local complex analytic diffeomorphisms for {n=2,3,4,5} .

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Representations of Solvable Groups

10.1017/cbo9780511525971 ◽

1993 ◽

Cited By ~ 107

Author(s):

Olaf Manz ◽

Thomas R. Wolf

Keyword(s):

Solvable Groups

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Languages of nilpotent and solvable groups (extended abstract)

Automata, Languages and Programming - Lecture Notes in Computer Science ◽

10.1007/3-540-09510-1_49 ◽

1979 ◽

pp. 616-632 ◽

Cited By ~ 4

Author(s):

Denis Thérien

Keyword(s):

Solvable Groups

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5 Rigid solvable groups. Algebraic geometry and model theory

Groups and Model Theory ◽

10.1515/9783110719710-005 ◽

2021 ◽

pp. 193-230

Author(s):

Nikolay Romanovskii

Keyword(s):

Algebraic Geometry ◽

Model Theory ◽

Solvable Groups

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𝒫-characters and the structure of finite solvable groups

Journal of Group Theory ◽

10.1515/jgth-2020-0087 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Jiakuan Lu ◽

Kaisun Wu ◽

Wei Meng

Keyword(s):

Finite Group ◽

Maximal Subgroup ◽

Solvable Group ◽

Irreducible Character ◽

Solvable Groups ◽

Irreducible Constituent ◽

A Finite Group

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

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