Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2021; 58(4): 1031-1038

Online first article May 7, 2021      Printed July 31, 2021

https://doi.org/10.4134/BKMS.b200809

Copyright © The Korean Mathematical Society.

On finite groups with the same order type as simple groups $\mathrm{F}_4(q)$ with $q$ even

Ashraf Daneshkhah, Fatemeh Moameri, Hosein Parvizi Mosaed

Bu-Ali Sina University; Bu-Ali Sina University; Alvand Institute of Higher Education

Abstract

The main aim of this article is to study quantitative structure of finite simple exceptional groups $\F_4(2^n)$ with $n>1$. Here, we prove that the finite simple exceptional groups $\F_4(2^n)$, where $2^{4n}+1$ is a prime number with $n>1$ a power of $2$, can be uniquely determined by their orders and the set of the number of elements with the same order. In conclusion, we give a positive answer to J. G. Thompson's problem for finite simple exceptional groups $\F_4(2^n)$.

Keywords: Exceptional groups of Lie type, prime graph, the set of the number of elements with the same order

MSC numbers: Primary 20D60; Secondary 20D06