Solvable conjugacy class graph of groups

2021/12/05 by Bhowal, Parthajit, Cameron, Peter J., Nath, Rajat Kanti +1
#05C25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2112.02613

Abstract

In this paper we introduce the graph Γ_sc(G) associated with a group G, called the solvable conjugacy class graph (abbreviated as SCC-graph), whose vertices are the nontrivial conjugacy classes of G and two distinct conjugacy classes C, D are adjacent if there exist x ∈ C and y ∈ D such that ⟨ x, y⟩ is solvable. We discuss the connectivity, girth, clique number, and several other properties of the SCC-graph. One of our results asserts that there are only finitely many finite groups whose SCC-graph has given clique number~d, and we find explicitly the list of such groups with d=2.

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