Address:
Corresponding author: Behnam Ebrahimzadeh, Department of Mathematics, Buinzahra Branch, Islamic Azad University, Buin Zahra, Iran
Reza Mohammadyari, Department of Mathematics, Buinzahra Branch, Islamic Azad University, Buin Zahra, Iran
E-mail:
behnam.ebrahimzadeh@gmail.com
rezamohammadyari@gmail.com
Abstract: One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups $Sz(q)$, where $q\pm \sqrt{2q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order.
AMSclassification: primary 20D06; secondary 20D60.
Keywords: element order, prime graph, Suzuki group.
DOI: 10.5817/AM2019-1-17