Publication details
Genus and crosscap of solvable conjugacy class graphs of finite groups
- authored by
- 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.
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- External Organisation(s)
-
Tezpur University
Cachar College
University of St. Andrews
- Type
- Article
- Journal
- Archiv der Mathematik
- No. of pages
- 15
- ISSN
- 0003-889X
- Publication date
- 24.03.2024
- Publication status
- E-pub ahead of print
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Mathematics(all)
- Electronic version(s)
-
https://doi.org/10.1007/s00013-024-01974-2 (Access:
Closed)
