Large orbits of nilpotent subgroups of linear groups

Yuchen Xu; Yong Yang

Large orbits of nilpotent subgroups of linear groups

Group Theory 2026-01-22 v1

Authors: Yuchen Xu , Yong Yang

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 $|N|$ .

Keywords

nilpotent subgroup linear groups finite solvable group G-module centralizer

Cite

@article{arxiv.2601.14618,
  title  = {Large orbits of nilpotent subgroups of linear groups},
  author = {Yuchen Xu and Yong Yang},
  journal= {arXiv preprint arXiv:2601.14618},
  year   = {2026}
}

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