Akbari, Banafsheh; Chuharski, Jake; Sharan, Vismay; Slonim, Zachary Characterization of Solubilizers of Elements in Minimal Simple Groups. arXiv:2309.09104 Preprint, arXiv:2309.09104 [math.GR] (2023). Summary: 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. MSC: 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D08 Simple groups: sporadic groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups × Cite Format Result Cite Full Text: arXiv OA License arXiv data are taken from the arXiv OAI-PMH API. If you found a mistake, please report it directly to arXiv.