具有给定霍尔常内含子群的有限群

IF 1.1 4区数学 Q1 MATHEMATICS

Ricerche di Matematica Pub Date : 2024-03-06 DOI:10.1007/s11587-024-00850-z

Xuanli He, Qinhui Sun, Jing Wang

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引用次数: 0

摘要

让 G 是一个有限群。如果 G 的一个子群 H 是常闭 \(H^G\) 的一个霍尔子群，那么这个子群就叫做霍尔常嵌于 G。在本文中，我们将 G 的 Sylow p 子群 P 的子群 D 定为 \(1<|D|<|O_p(G)|\)，并在假设 P 的所有阶为 \(|H|=|D|\)的子群 H 都是霍尔常嵌于 G 的情况下研究 G 的结构。

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Finite group with given Hall normally embedded subgroups

Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of the normal closure \(H^G\). In this paper, we fix a subgroup D of Sylow p-subgroup P of G with \(1<|D|<|O_p(G)|\) and study the structure of G under the assumption that all subgroups H of P with order \(|H|=|D|\) are Hall normally embedded in G.

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来源期刊

Ricerche di Matematica Mathematics-Applied Mathematics

CiteScore

3.00

自引率

8.30%

发文量

期刊介绍： “Ricerche di Matematica” publishes high-quality research articles in any field of pure and applied mathematics. Articles must be original and written in English. Details about article submission can be found online.