Solvable conjugacy class graph of groups

verfasst von

Parthajit Bhowal, Peter J. Cameron, Rajat Kanti Nath, Benjamin Sambale

Abstract

In this paper we introduce the graph $\Gamma_{sc}(G)$ 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 $x \in C$ and $y \in D$ such that $\langle x, y\rangle$ 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 $d=2$.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Preprint

Publikationsdatum

05.12.2021

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Elektronische Version(en)

http://arxiv.org/abs/2112.02613v3 (Zugang: Offen)