Large orbits of nilpotent subgroups of linear groups

Yuchen Xu; Yong Yang

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arXiv · 2601.14618

Large orbits of nilpotent subgroups of linear groups

Yuchen Xu·Yong Yang

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Abstract

Suppose that $G$ is a finite solvable group and $V$ is a finite, faithful and completely reducible $G$-module. Let $N$ be a nilpotent subgroup of $G$, then there exits $v \in V$ such that $|\bC_N(v)| \leq (|N|/p)^{1/p}$, where $p$ is the smallest prime divisor of $|N|$.

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Yuchen Xu, Yong Yang. 2026-01-21. Large orbits of nilpotent subgroups of linear groups. https://arxiv.org/abs/2601.14618

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