Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups

Pub Date : 2024-01-30 DOI:10.1515/gmj-2024-2001

Yifan Liu, Jiangtao Shi

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引用次数: 0

Abstract

Let A and G be finite groups such that A acts coprimely on G by automorphisms. We prove that if every self-centralizing non-nilpotent A-invariant subgroup of G is a TI-subgroup or a subnormal subgroup, then every non-nilpotent A-invariant subgroup of G is subnormal and G is p-nilpotent or p-closed for any prime divisor p of | G |

{|G|}

. If every self-centralizing non-metacyclic A-invariant subgroup of G is a TI-subgroup or a subnormal subgroup, then every non-metacyclic A-invariant subgroup of G is subnormal and G is solvable.

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其中某些特定不变子群是 TI 子群或子法向子群的有限群

设 A 和 G 都是有限群，且 A 通过自动形共同作用于 G。我们证明，如果 G 的每个自中心化非零能 A 不变子群都是 TI 子群或子正常子群，那么 G 的每个非零能 A 不变子群都是子正常的，并且对于 | G | {|G|} 的任何素除数 p，G 都是 p 零能或 p 封闭的。如果 G 的每个自中心化非元胞 A 不变子群都是 TI 子群或子正常子群，那么 G 的每个非元胞 A 不变子群都是子正常的，并且 G 是可解的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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