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

Nader Mahmoud Taffach | Zendy

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A 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.

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