The Commuting Graph of a Solvable A-Group

2024/01/30 by Rachel Carleton, Mark L. Lewis, Carleton, Rachel +1 · 1 citation
Engineering · Mathematics · #05C25 (Secondary) #20D20 (Primary) #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.10927

openalex publication_date 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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