On finite groups with the same order type as simple groups F4 (q) with q even
Bull. Korean Math. Soc.
Published online May 7, 2021
Ashraf Daneshkhah, Fatemeh Moameri, and Hosein Parvizi Mosaed
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 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 order 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 : 20D60
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