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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 &lt; q &lt; r are different primes.

journal of mathematics

Finite Groups of Order <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>p</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </math>qr in which the Number of Elements of Maximal Order Is <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <msup> <mrow> <mi>p</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msup> <mi>q</mi> <mi>∗</mi> </math>

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

Finite Groups of Order $p^{2}$ qr in which the Number of Elements of Maximal Order Is $p^{3} q *$