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http://dx.doi.org/10.4134/BKMS.b200809

ON FINITE GROUPS WITH THE SAME ORDER TYPE AS SIMPLE GROUPS F4(q) WITH q EVEN  

Daneshkhah, Ashraf (Department of Mathematics Faculty of Science Bu-Ali Sina University)
Moameri, Fatemeh (Department of Mathematics Faculty of Science Bu-Ali Sina University)
Mosaed, Hosein Parvizi (Alvand Institute of Higher Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 1031-1038 More about this Journal
Abstract
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).
Keywords
Exceptional groups of Lie type; prime graph; the set of the number of elements with the same order;
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