Normality Of Quartic Cayley Graphs On Regular p-Groups: A CFSG-Free Approach
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908972983779328 |
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| author | Kutnar, Klavdija Malnič, Aleksander Marušič, Dragan |
| author_facet | Kutnar, Klavdija Malnič, Aleksander Marušič, Dragan |
| contents | Relying on the Classification of Finite Simple Groups it was shown by Feng and Xu (Discrete Math., 2005) that every quartic Cayley graph of a regular $p$-group, $p \neq 2,5$, is normal. In this paper a CFSG-free proof of Feng-Xu theorem is given. Along the way it is also proved that for an arbitrary $p$-group $G$ with a minimum set $\{a,b\}$ of two generators, in the corresponding Cayley graph $\mathrm{Cay}(G,\{a,a^{-1},b,b^{-1}\})$ the induced action of vertex stabilizer on the neighbors' set is contained in the dihedral group $D_8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10220 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normality Of Quartic Cayley Graphs On Regular p-Groups: A CFSG-Free Approach Kutnar, Klavdija Malnič, Aleksander Marušič, Dragan Combinatorics Group Theory 05C25 Relying on the Classification of Finite Simple Groups it was shown by Feng and Xu (Discrete Math., 2005) that every quartic Cayley graph of a regular $p$-group, $p \neq 2,5$, is normal. In this paper a CFSG-free proof of Feng-Xu theorem is given. Along the way it is also proved that for an arbitrary $p$-group $G$ with a minimum set $\{a,b\}$ of two generators, in the corresponding Cayley graph $\mathrm{Cay}(G,\{a,a^{-1},b,b^{-1}\})$ the induced action of vertex stabilizer on the neighbors' set is contained in the dihedral group $D_8$. |
| title | Normality Of Quartic Cayley Graphs On Regular p-Groups: A CFSG-Free Approach |
| topic | Combinatorics Group Theory 05C25 |
| url | https://arxiv.org/abs/2604.10220 |