Characterization of Solubilizers of Elements in Minimal Simple Groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916178781274112 |
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| author | Akbari, Banafsheh Chuharski, Jake Sharan, Vismay Slonim, Zachary |
| author_facet | Akbari, Banafsheh Chuharski, Jake Sharan, Vismay Slonim, Zachary |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_09104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterization of Solubilizers of Elements in Minimal Simple Groups Akbari, Banafsheh Chuharski, Jake Sharan, Vismay Slonim, Zachary Group Theory 20D10, 20D08, 20D60 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. |
| title | Characterization of Solubilizers of Elements in Minimal Simple Groups |
| topic | Group Theory 20D10, 20D08, 20D60 |
| url | https://arxiv.org/abs/2309.09104 |