Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(3): 651-656

Printed May 31, 2016

https://doi.org/10.4134/BKMS.b140564

Copyright © The Korean Mathematical Society.

Characterization of suzuki group by nse and order of group

Ali Iranmanesh, Hosein Parvizi Mosaed, and Abolfazl Tehranian

Tarbiat Modares University, Islamic Azad University, Islamic Azad University

Abstract

Let $G$ be a finite group and $\nse(G)$ be the set of numbers of elements of $G$ of the same order. In this paper, we prove that the simple group $Sz(2^{2m+1})$, where $2^{2m+1}-1$ is a prime number, is uniquely determined by $\nse(Sz(2^{2m+1}))$ and $|Sz(2^{2m+1})|$.

Keywords: set of the numbers of elements of the same order, Suzuki group

MSC numbers: Primary 20D60; Secondary 20D06

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