Non-inner automorphisms of order $p$ in finite $p$-groups admitting cyclic center
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909603082534912 |
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| author | Ma, Xuesong Xu, Wei |
| author_facet | Ma, Xuesong Xu, Wei |
| contents | Let $G$ be a finite non-abelian $p$-group admitting cyclic center and $p$ be an odd prime. In this paper, we prove that if $C_{G}(Z(γ_{3}(G)G^{p}))\nleqslantγ_{3}(G)G^{p}$, then $G$ has a non-inner automorphism of order $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-inner automorphisms of order $p$ in finite $p$-groups admitting cyclic center Ma, Xuesong Xu, Wei Group Theory 20D15 Let $G$ be a finite non-abelian $p$-group admitting cyclic center and $p$ be an odd prime. In this paper, we prove that if $C_{G}(Z(γ_{3}(G)G^{p}))\nleqslantγ_{3}(G)G^{p}$, then $G$ has a non-inner automorphism of order $p$. |
| title | Non-inner automorphisms of order $p$ in finite $p$-groups admitting cyclic center |
| topic | Group Theory 20D15 |
| url | https://arxiv.org/abs/2505.04125 |