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.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
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)
- Creator
-
Carleton, Rachel
Lewis, Mark L.
- DOI
-
10.1515/jgth-2023-0076
- URN
-
urn:nbn:de:101:1-2501041702048.851735197670
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
15.08.2025, 7:23 AM CEST
Data provider
This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Carleton, Rachel
- Lewis, Mark L.
Other Objects (12)
Solvable conjugacy class graph of groups
Group order and element orders in solvable groups
On the construction of number fields with solvable Galois group
Fast Parameterized Preprocessing for Polynomial-Time Solvable Graph Problems
On the structure of a representation of a finite solvable group
An exactly solvable model of the Calogero type for the icosahedral group
The commuting distribution
The Commuting Distribution
The commuting island
Solvable polynomial rings
Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups
Spectrum of super commuting graphs of some finite groups
Solvable conjugacy class graph of groups
Group order and element orders in solvable groups
On the construction of number fields with solvable Galois group
Fast Parameterized Preprocessing for Polynomial-Time Solvable Graph Problems
On the structure of a representation of a finite solvable group
An exactly solvable model of the Calogero type for the icosahedral group
The commuting distribution
The Commuting Distribution
The commuting island
Solvable polynomial rings
Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups
Spectrum of super commuting graphs of some finite groups
Solvable conjugacy class graph of groups
Group order and element orders in solvable groups
On the construction of number fields with solvable Galois group
Fast Parameterized Preprocessing for Polynomial-Time Solvable Graph Problems
On the structure of a representation of a finite solvable group
An exactly solvable model of the Calogero type for the icosahedral group
The commuting distribution
The Commuting Distribution
The commuting island
Solvable polynomial rings
Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups