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)