A Study About One Generation of Finite Simple Groups and Finite Groups

Nader Taffach

Journal of Mathematics Research, 2021, vol. 13, issue 3, 59

Abstract: In this paper, we study the problem of how a finite group can be generated by some subgroups. In order to the finite simple groups, we show that any finite non-abelian simple group can be generated by two Sylow p1 - and p_2 -subgroups, where p_1 and p_2 are two different primes. We also show that for a given different prime numbers p and q , any finite group can be generated by a Sylow p -subgroup and a q -subgroup.

Date: 2021
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