Publikationsdetails

Genus and crosscap of solvable conjugacy class graphs of finite groups

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

The solvable conjugacy class graph of a finite group G, denoted by Γsc(G), is a simple undirected graph whose vertices are the non-trivial 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. In this paper, we discuss certain properties of the genus and crosscap of Γsc(G) for the groups D2n, Q4n, Sn, An, and PSL(2,2d). In particular, we determine all positive integers n such that their solvable conjugacy class graphs are planar, toroidal, double-toroidal, or triple-toroidal. We shall also obtain a lower bound for the genus of Γsc(G) in terms of the order of the center and number of conjugacy classes for certain groups. As a consequence, we shall derive a relation between the genus of Γsc(G) and the commuting probability of certain finite non-solvable group.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Externe Organisation(en)
Tezpur University
Cachar College
University of St. Andrews
Typ
Artikel
Journal
Archiv der Mathematik
Band
122
Seiten
475-489
Anzahl der Seiten
15
ISSN
0003-889X
Publikationsdatum
05.2024
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Mathematik (insg.)
Elektronische Version(en)
https://doi.org/10.1007/s00013-024-01974-2 (Zugang: Geschlossen)