Euclid's Algorithm

Direct Sum

Union and Intersection of Subspaces

Sum of Subspaces

7 Common Example of Group of order 4

Cayley Graph of Dihedral Group D3

Order 4 Groups and their Cayley Tables

Abstract Algebra Review

Groups of order 6

Cyclic Group of Order 6

Homomorphism z6 vs U7

Row Column Null Span Space

Z12 and its subgroups

Understanding Composition of Permutations and Product of Transpositions

Groups of Order 4

For Order 4 there are basically two types of group. Klien 4 and Cyclic Group of order 4. In Klien 4 each element is its own inverse. In cyclic group there are two elements which are inverse of each other and there are two which are their own inverses. The two which are inverse of each other are also the generator of this cyclic group.

S4 and Dihedral Group group D4

Flipping and Rotation of Dihedral Group

Dihedral group of Square

Homomorphism Z6 vs U7 example

One should notice that just finding a bijective mapping doesn't define a homomorphism (or isomorphism). The mapping should satisfy f(x+y)=f(x)*f(y) to be a homomorphism.

Summary of Group theory on August 4 2017