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math.GR2024★ 1 cited
The Commuting Graph of a Solvable A-Group
Rachel Carleton, Mark Lewis
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…
math.GR2024
Finite solvable tidy Groups whose orders are divisible by two primes
Nicolas F. Beike, Rachel Carleton, David G. Costanzo +4
In this paper, we investigate finite solvable tidy groups. We classify the tidy -groups. Combining this with a previous result, we are able to characterize the finite t…
math.GR2021
Extending Morgan and Parker's results about commuting graphs
Nicolas F. Beike, Rachel Carleton, David G. Costanzo +4
Morgan and Parker have proved that if is a group satisfying the condition that , then the connected components of the commuting graph of have diameter at most $10…