Finite groups whose order graph is C4-free
Year: 2025
Type: article
Abstract: Given a finite group G , the order graph of G, denoted by S(G), is a graph whose vertex set is G, and two distinct vertices a and b are adjacent if o(a) | o(b) or o(b) | o(a), where o(a), and o(b), are the orders of a and b in G, respectively. In this paper, by the order of an element, we give a characterization of the finite groups whose order graph is C4-free. As applications, we classify a few families of finite groups whose order graph is C4-free, such as nilpotent groups, dihedral groups and symmetric groups.
Authors: Jin Chen, Jie Chen, Shixun Lin
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $539
OpenAlex ID: W4414913383