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

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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I, Roshan Kumar Jaiswal, welcome you on your TH-cam channel eMaths Guru.
This concept is very important to crack TGT/PGT/CSIR NET & equally important in getting good marks in university examinations like B.Sc/M.Sc/B.Tech.
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1- Definition of Groups, Algebraic structure, Grupoid, Monoid
• Group Theory | Groupoi...
2- abelian groups with solved examples
• Group Theory | Abelian...
3-Addition Modulo and Multiplication Modulo
• Group Theory | Additio...
4-Properties of a Group
• Group Theory | Propert...
5- Order of a group and some important theorems
• Group Theory | Order o...
6- Subgroups and some important theorems
• Group Theory | Subgrou...
7- Cyclic group with examples
• Group Theory | Cyclic ...
8-Cyclic groups theorems
• Group Theory | Cyclic ...
9-Cosets definition and examples
• Group Theory | Cosets ...
10- Cosets | some important theorems| Lagrange’s theorem
• Group Theory| Cosets T...
11- Normal subgroups definition with solved examples
• Group Theory| Normal S...
12- Normal Subgroups Some Important theorems
• Group Theory| Normal S...
13- Quotient Groups with solved examples
• Group Theory | Quotien...
14-Homomorphism definition and examples
• Group Theory | Homomor...
15- Kernel of homomorphism
• Group Theory| Kernel o...
16- Isomorphism definition with examples
• Group Theory | Isomorp...
17- Fundamental theorem of Group homomorphism ( First theorem of Isomorphism )
• Group Theory | Fundame...
18- permutation group or symmetric group
• Group Theory | Permuta...
19- circular permutation
• Group Theory | Circula...
20- Second theorem of Isomorphism
• Group Theory | Second ...
21- Third theorem of Isomorphism
• Group Theory | The Thi...
22- Automorphisms of a group
• Group Theory | Automor...
23- Theorem of automorphism
• Group Theory | Theorem...
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Thank you
Roshan Kumar Jaiswal
Assistant Teacher
Govt. Basic Education U.P.

[@abhaygupta4461]

Very nice explanation 😊😊😊

[@savitakumarimeena9756]

Thanks sir bhut acha padaya

[@khemrajchaulagai6855]

thank you sir.I'm from nepal.i mostly liked your teaching method and i understood clearly.

[@tajuddints1231]

I can't explain about your way of explanation ❤️❤️

[@abhaygupta4461]

Thanks sir 😊😊😊😊

[@shobhanakushwaha2649]

Your teaching style is very good

[@shobhanakushwaha2649]

Nice one sir

[@ishwarlal9271]

Very nice sir

[@debasishsaikia9877]

Kis book se padha rhe ho sir

[@somansoman8162]

Tnk u so much sir

[@ashokbhati7692]

Nice

[@user-708]

Sir important b bta diya kry theorem or question important

[@eMathsGuru]

Okk sure..

[@araj5720]

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