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.
Ashraf Daneshkhah, Fatemeh Moameri, Hosein Parvizi Mosaed
Bu-Ali Sina University; Bu-Ali Sina University; Alvand Institute of Higher Education
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
2013; 50(1): 117-123
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