Finite Groups of Order p 2 qr in which the Number of Elements of Maximal Order Is p 3 q ∗

Abstract

Let $G$ be a finite group. We know that the order of $G$ and the number of elements of maximal order in $G$ are closely related to the structure of $G$ . This topic involves Thompson’s conjecture. In this paper, we classify the finite groups of order $p^{2}qr$ in which the number of elements of maximal order is $p^{3}q$ , where $p<q<r$ are different primes.