Introduction to Abstract Algebra: Group Theory
Learn group theory or abstract algebra in pure mathematics with examples and solved exercises
3.92 (30 reviews)
1,220
students
10 hours
content
Aug 2021
last update
$54.99
regular price
What you will learn
Groups and related examples
Identity element is the only elements which is idempotent
Cancellation law hold in a group G
Definition of Subgroups and related examples
H is subgroup Iff ab^-1 is contained in H
Intersection of any collection of subgroups is subgroup
HuK is subgroup iff H is contained in K or K is contained in H
Cyclic group and related examples
Every subgroup of a cyclic group is cyclic
Definition of cosets and related examples
Prove that the number of left or right cosets define the partition of a group G
Statement and Proof of Lagrange's Theorem
Symmetric groups and related examples and exercises
Group of querternian and Klein's four group
Normalizers, centralizers and center of a group G and related theorem and examples
Quotient or Factor groups
Derived groups and related many examples
Normal Subgroups, conjugacy classes, conjugate subgroups and related examples and theorems
Kernal of group
Automorphism and inner automorphism
P Group and related theorems and examples
Relations in group like homomorphism and isomorphism
The centralizers is a subgroup of a group G
The normalizers is a subgroup of a group G
Center of a group is a subgroup of a group G
The relation of conjugacy is an equivalence relation
Theorem and examples on quotient groups
Double cosets and related examples
Definition of automorphism
What is an inner automorphism
Every cyclic group is an abelian group
Groups of residue classes on different mode
Examples of D_4 and D_5 groups
Examples related C_6 and V_4
The first isomorphism theorem and its proof
The 2nd isomorphism theorem and its proof
The 3rd isomorphism theorem and its proof
Direct product of cyclic group
Ring and Field
Zero Divisor
Integral Domain
Theorems on Ring and Field
Screenshots
Related Topics
2451508
udemy ID
7/9/2019
course created date
11/21/2019
course indexed date
Bot
course submited by