The Commuting Graph of a Solvable A-Group
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910334619484160 |
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| author | Carleton, Rachel Lewis, Mark |
| author_facet | Carleton, Rachel Lewis, Mark |
| contents | Let $G$ be a finite group. Recall that an $A$-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable $A$-group. Assuming that the commuting graph is connected, we show when the derived length of $G$ is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Commuting Graph of a Solvable A-Group Carleton, Rachel Lewis, Mark Group Theory 20D20 (Primary), 05C25 (Secondary) Let $G$ be a finite group. Recall that an $A$-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable $A$-group. Assuming that the commuting graph is connected, we show when the derived length of $G$ is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved. |
| title | The Commuting Graph of a Solvable A-Group |
| topic | Group Theory 20D20 (Primary), 05C25 (Secondary) |
| url | https://arxiv.org/abs/2402.10927 |