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arXiv · 2510.22474

Large orbits of Hall subgroups of solvable linear groups

Samarth Das·Yong Yang
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Abstract

Suppose that $G$ is a finite solvable group and let $H$ be a Hall $\pi$-subgroup, let $b(H)$ be the largest character degree of $H$, we show that $|G:O_{\pi' \pi}(G)|_{\pi} \leq b(H)^2$.

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Samarth Das, Yong Yang. 2025-10-26. Large orbits of Hall subgroups of solvable linear groups. https://arxiv.org/abs/2510.22474

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