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

Source 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 q r in which the number of elements of maximal order is p 3 q , where p < q < r are different primes.