Open AccessA Study About One Generation of Finite Simple Groups and Finite Groups
Author(s) -
Nader Mahmoud Taffach
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n3p59
Subject(s) - sylow theorems , mathematics , simple group , p group , classification of finite simple groups , locally finite group , simple (philosophy) , finite group , abelian group , ca group , prime (order theory) , omega and agemo subgroup , combinatorics , order (exchange) , group (periodic table) , group of lie type , pure mathematics , elementary abelian group , torsion subgroup , group theory , physics , economics , philosophy , epistemology , finance , quantum mechanics
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.