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arXiv · 2309.09104

Characterization of Solubilizers of Elements in Minimal Simple Groups

Banafsheh Akbari·Jake Chuharski·Vismay Sharan·Zachary Slonim
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Abstract

Given a finite group $G$, the solubilizer of an element $x$, denoted by $\Sol_G(x)$, is the set of all elements $y$ such that $\langle x, y\rangle$ is a soluble subgroup of $G$. In this paper, we provide a classification for all solubilizers of elements in minimal simple groups. We also examine these sets to explore their properties by discussing some computational methods and making some conjectures for further work.

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Banafsheh Akbari, Jake Chuharski, Vismay Sharan, Zachary Slonim. 2023-09-16. Characterization of Solubilizers of Elements in Minimal Simple Groups. https://arxiv.org/abs/2309.09104

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