• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1031-1038
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• 2021

The main aim of this article is to study quantitative structure of finite simple exceptional groups F₄(2ⁿ) with n > 1. Here, we prove that the finite simple exceptional groups F₄(2ⁿ), where 2⁴ⁿ + 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 F₄(2ⁿ).