Large orbits of nilpotent subgroups of linear groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866918298640187392 |
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| author | Xu, Yuchen Yang, Yong |
| author_facet | Xu, Yuchen Yang, Yong |
| contents | 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 $|N|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14618 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large orbits of nilpotent subgroups of linear groups Xu, Yuchen Yang, Yong Group Theory 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 $|N|$. |
| title | Large orbits of nilpotent subgroups of linear groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2601.14618 |