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The impact of the solubilizer of an element on the structure of a finite group

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arxiv 2210.11564 v3 pith:DAOAM3R4 submitted 2022-10-20 math.GR

Hamid Mousavi , Mina Poozesh , Yousef Zamani This is my paper
classification math.GR
keywords groupelementfinitestructuredenotegeneratedimpactinfluence
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abstract

Let $G$ be a finite group, and let $x$ be an element of $G$. Denote by $\Sol_G(x)$ the set of all $y \in G$ such that the group generated by $x$ and $y$ is soluble. We investigate the influence of $\Sol_G(x)$ on the structure of $G$.

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