Let π (G) denote the set of prime divisors of the order of a finite group G. The prime graph of
G, denoted Γ G, is the graph with vertex set π (G) with edges {p, q}∈ E (Γ G) if and only if …

Huppert's ρ‐σ conjecture is one of the main open problems on character degrees of finite
groups. A number of ρ‐σ problems have been studied. For instance, T. Keller and J. Zhang …

Let G be a finite group and χ be a character of G, we denote the codegree of χ to be codeg
(χ)=| G: ker⁡ χ| χ (1). We define σ (codeg (G))= max⁡{| π (codeg (χ))|| χ∈ Irr (G)} where π …

The spectrum of a finite group is the set of its element orders. We give an affirmative answer
to Problem 20.58 (a) from the Kourovka Notebook proving that for every positive integer k …

Let G be a finite group and be a character of G. The codegree of is. We write for the set of
prime divisors of, for the set of prime divisors of and. We show that. This improves the main …

Let ρ (n) ρ(n) denote the maximal number of different primes that may occur in the order of a
finite solvable group G, all elements of which have orders divisible by at most n distinct …

On the prime divisors of element orders - Hung - 2021 - Mathematische Nachrichten - Wiley
Online Library Skip to Article Content Skip to Article Information Wiley Online Library Wiley …

Let G be a finite group. For an irreducible character χ of G, the number χ c (1)=[G: ker χ] χ (1)
is called the co-degree of χ. Let Codeg (G) denote the set of co-degrees of the irreducible …

ON THE NUMBER OF DIFFERENT PRIME DIVISORS OF ELEMENT ORDERS 1. Introduction
Given a finite group G, let ρ(G) be the number of d Page 1 PROCEEDINGS OF THE AMERICAN …

In this paper, we summarize the work on the characterization of finite simple groups and the
study on finite groups with``the set of element orders" and``two orders"(the order of group …