On finite groups with the same order type as simple groups $\mathrm{F}_4(q)$ with $q$ even
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 1031-1038
Published online May 7, 2021
Printed July 31, 2021
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
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