Group Theory || Theorem on External Direct Product of Groups || Direct Product || Abstract Algebra

Описание: Hello students,
This video lecture of Group theory by Roshan Sir will help you to understand the following topics in Mathematics:
Group Theory | Theorems on Direct Products of Groups | | Abstract Algebra
1- If G1 and G2 are two groups, then the subsets G1x{e2} and {e1}xG2 are normal subgroups of G1xG2 isomorphic to G1 and G2 respectively.
2- If G1 and G2 are two groups, then
(i) G1x{e2} Ո {e1}xG2 = { (e1,e2) }
(ii) every element in G1x{e2} commutes with element in {e1}xG2
(iii) every element in G1xG2 can be uniquely expressed as the products of element in G1x{e2} by element in {e1}xG2.
(iv) G1xG2 ≌ G2xG1

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Roshan Kumar Jaiswal
Assistant Teacher
Govt. Basic Education U.P.