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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2602.13354 |
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| _version_ | 1866908834451161088 |
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| author | Chen, Gang Zhao, Wenhua |
| author_facet | Chen, Gang Zhao, Wenhua |
| contents | Let $p$ be a prime, $e$ a nonnegative integer, and G a finite p-group with $p^{e+1}$ dividing $|G|$. Let I be the intersection of all subgroups of order $p^{e+1}$ in $G$. It is proved that $|I\cap Z(G)|\le |π_0(Γ_{p,e}(G))|\le {\rm Irr}(I)$, where $Γ_{p,e}(G)$, whose connected components is denoted by $π_0(Γ_{p,e}(G))$, is the poset consisting of all pairs $(H, φ)$ with $H \le G$, $|H|\ge p^{e+1}$, and $φ\in {\rm Irr}(H)$. Hence, an affirmative answer to Question 2 raised by Meng and Yang is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An affirmative answer to a question on connectivity of p-subgroup posets with irreducible characters Chen, Gang Zhao, Wenhua Group Theory 20C05, 20D15 Let $p$ be a prime, $e$ a nonnegative integer, and G a finite p-group with $p^{e+1}$ dividing $|G|$. Let I be the intersection of all subgroups of order $p^{e+1}$ in $G$. It is proved that $|I\cap Z(G)|\le |π_0(Γ_{p,e}(G))|\le {\rm Irr}(I)$, where $Γ_{p,e}(G)$, whose connected components is denoted by $π_0(Γ_{p,e}(G))$, is the poset consisting of all pairs $(H, φ)$ with $H \le G$, $|H|\ge p^{e+1}$, and $φ\in {\rm Irr}(H)$. Hence, an affirmative answer to Question 2 raised by Meng and Yang is obtained. |
| title | An affirmative answer to a question on connectivity of p-subgroup posets with irreducible characters |
| topic | Group Theory 20C05, 20D15 |
| url | https://arxiv.org/abs/2602.13354 |