A note on conjugacy of supplements in soluble periodic linear groups

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-08-04 DOI:10.1515/forum-2024-0102

Marco Trombetti

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引用次数: 0

Abstract

The aim of this short note is to prove that if G is a (homomorphic images of a) soluble periodic linear group and N is a locally nilpotent normal subgroup of G such that N and G / N

{G/N}

have no isomorphic G-chief factors, then two supplements to N in G are conjugate provided that they have the same intersection with N. This result follows from well-known theorems in the theory of Schunck classes (see [A. Ballester-Bolinches and L. M. Ezquerro, On conjugacy of supplements of normal subgroups of finite groups, Bull. Aust. Math. Soc. 89 2014, 2, 293–299]), and it appeared as the main theorem of [C. Parker and P. Rowley, A note on conjugacy of supplements in finite soluble groups, Bull. Lond. Math. Soc. 42 2010, 3, 417–419].

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关于可溶性周期线性群中的共轭补充物的说明

本短文旨在证明，如果 G 是可溶周期线性群的（同态图像），而 N 是 G 的局部零potent 正则子群，使得 N 和 G / N {G/N} 没有同构的 G 主因，那么 G 中 N 的两个补充群是共轭的，条件是它们与 N 有相同的交集。这一结果源于 Schunck 类理论中的著名定理（见 [A. Ballester-Bolinches and L. M. Ezquerro, On conjugacy of supplements to N in G, Bull.Ballester-Bolinches and L. M. Ezquerro, On conjugacy of supplements of normal subgroups of finite groups, Bull. Aust.Aust.Math.89 2014, 2, 293-299]），并作为主定理出现在[C.Parker and P. Rowley, A note on conjugacy of supplements in finite soluble groups, Bull.Lond.Math.42 2010, 3, 417-419].

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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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.