Expansion of normal subsets of odd-order elements in finite groups

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2026-04-06 DOI:10.1112/jlms.70534

Chris Parker, Jack Saunders

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引用次数: 0

Abstract

Let $G$ be a finite group and $K$ a normal subset consisting of odd-order elements. The rational closure of $K$ , denoted $D_{K}$ , is the set of elements $x \in G$ with the property that $⟨ x ⟩ = ⟨ y ⟩$ for some $y$ in $K$ . If $K^{2} \subseteq D_{K}$ , we prove that $⟨ K ⟩$ is soluble.

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有限群中奇阶元素正规子集的展开

设G$ G$是一个有限群，K$ K$是一个由奇阶元素组成的正规子集。K$ K$的有理闭包，表示为D K$ \mathbf {D}_K$，G$中的元素x∈G$ x \是否具有⟨x⟩=⟨y⟩$\langle x \rangle = \langle y \rangle$的性质y$ y$在K$ K$中。若K 2≥K$ K^2 \subseteq \mathbf {D}_K$，我们证明⟨K⟩$\ rangle$是可解的。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.