Group Theory | Inner Automorphisms | Theorem of Inner automorphism | Abstract Algebra |

Hello students,
This video lecture on Group theory by Roshan Sir will help you to understand the following topics in Mathematics:
Group Theory | Inner automorphisms of a Group | Definition with theorems | Abstract Algebra
1- Let a be a fixed element of a group G. Then the mapping fa : G⟶G defined by
fa (x) = a-1xa ⍱ xεG.
2- Definition of Inner Automorphism
3- For an abelian group, the only inner automorphism is the identity mapping whereas for non-abelian groups there exist non-trivial automorphisms.
4- The set I(G) of all inner automorphisms of a group G is a normal subgroup of the group of its automorphisms isomorphic to the quotient group G/Z of G where Z is the centre of G.

#GroupTheory #Inner_Automorphisms_of_a_Group #Abstract Algebra

-----------Content of the Video--------------
00:00 – Intro
01:01 – Theorem of inner automorphisms
10:25 – Definition of inner automorphism
13:13 – Theorem 1
20:18 – Theorem 2
I, Roshan Kumar Jaiswal, welcome you on your YouTube channel eMaths Guru.

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1- Definition of Groups, Algebraic structure, Grupoid, Monoid

2- abelian groups with solved examples

3-Addition Modulo and Multiplication Modulo

4-Properties of a Group

5- Order of a group and some important theorems

6- Subgroups and some important theorems

7- Cyclic group with examples

8-Cyclic groups theorems

9-Cosets definition and examples

10- Cosets | some important theorems| Lagrange’s theorem

11- Normal subgroups definition with solved examples

12- Normal Subgroups Some Important theorems

13- Quotient Groups with solved examples

14-Homomorphism definition and examples

15- Kernel of homomorphism

16- Isomorphism definition with examples

17- Fundamental theorem of Group homomorphism ( First theorem of Isomorphism )

18- permutation group or symmetric group

19- circular permutation

20- Second theorem of Isomorphism

21- Third theorem of Isomorphism

22- Automorphisms of a group

23- Theorem of automorphism

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