The Gill-Guillot commuting graph for sporadic and related groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915768756600832 |
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| author | Craven, David A. del Valle, Coen Parker, Chris |
| author_facet | Craven, David A. del Valle, Coen Parker, Chris |
| contents | Let $G$ be a finite group and $\mathcal{C}$ a normal subset of $G$. The Gill-Guillot graph has vertices $\mathcal C$ and $x, y \in \mathcal C$ are adjacent if and only if $x$ and $y$ commute and $\{xy^{-1},x^{-1}y\} \cap \mathcal C$ is non-empty. We study the connectivity of this graph for quasisimple groups with $G/Z(G)$ a sporadic simple group and for certain simple groups with exceptional Schur multiplier. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02032 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Gill-Guillot commuting graph for sporadic and related groups Craven, David A. del Valle, Coen Parker, Chris Group Theory Let $G$ be a finite group and $\mathcal{C}$ a normal subset of $G$. The Gill-Guillot graph has vertices $\mathcal C$ and $x, y \in \mathcal C$ are adjacent if and only if $x$ and $y$ commute and $\{xy^{-1},x^{-1}y\} \cap \mathcal C$ is non-empty. We study the connectivity of this graph for quasisimple groups with $G/Z(G)$ a sporadic simple group and for certain simple groups with exceptional Schur multiplier. |
| title | The Gill-Guillot commuting graph for sporadic and related groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2602.02032 |