The commuting graph of a solvable -group
Abstract: Let be a finite group. Recall that an -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 -group. Assuming that the commuting graph is connected, we show when the derived length of 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.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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The commuting graph of a solvable -group ; volume:28 ; number:1 ; year:2025 ; pages:165-178 ; extent:14
Journal of group theory ; 28, Heft 1 (2025), 165-178 (gesamt 14)
- Urheber
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Carleton, Rachel
Lewis, Mark L.
- DOI
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10.1515/jgth-2023-0076
- URN
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urn:nbn:de:101:1-2501041702048.851735197670
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:23 MESZ
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Beteiligte
- Carleton, Rachel
- Lewis, Mark L.
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