Normal sections, class sizes and solvability of finite groups

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Simplicity of normal subgroups and conjugacy class sizes

Beltrán

Felipe

2014

Monatsh Math

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A criterion for a normal subgroup to be hypercentral based on class sizes

Beltrán

2024

Ricerche mat

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Let G be a finite group and N a normal subgroup of G. We prove that the knowledge of the sizes of the conjugacy classes of G that are contained in N and of their multiplicities provides information of N in relation to the structure of G. Among other results, we obtain a criterion to determine whether a Sylow p-subgroup of N lies in the hypercentre of G for a fixed prime p, and therefore, whether the whole subgroup N is hypercentral in G.

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On ϕ-ideals and the structure of Lie algebras

Goudarzi

Riyahi

2020

J. Algebra Appl.

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This paper aims to study the concept of [Formula: see text]-ideals of a finite-dimensional Lie algebra which is analogous to the concept of [Formula: see text]-ideal and [Formula: see text]-normal subgroup. We compile some basic properties of [Formula: see text]-ideals and consider the influence of this concept on the structure of a finite-dimensional Lie algebra, especially its solvability and supersolvability. We also show that the counterpart of some results for [Formula: see text]-ideals of Lie algebras and [Formula: see text]-normal subgroups are not valid here.

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Normal sections, class sizes and solvability of finite groups

Cited by 3 publications

References 14 publications

Simplicity of normal subgroups and conjugacy class sizes

Simplicity of normal subgroups and conjugacy class sizes

A criterion for a normal subgroup to be hypercentral based on class sizes

On ϕ-ideals and the structure of Lie algebras

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