Year: 2025
Type: article
Abstract: For a finite group G, let π e (G) be the set of orders of its elements.The order classes of G, denoted as OC(G), are collections of pairs [k, m], where k ∈ π e (G) and m represents the number of elements in G with order k.Two finite groups G and H are said to be of the same order type if OC(G) = OC(H).It is unequivocal that two simple groups G 1 and G 2 with the same order classes are isomorphic.This paper presents counterexamples demonstrating that this property does not necessarily hold for non-simple groups.Furthermore, we will examine several properties of non-simple groups that derived from their group order and element orders, and address certain open problems related to these properties.
Authors: I.A. Jawarneh, B.N. Al-Hasanat
Institution: Al-Hussein Bin Talal University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410276641