# Tag: Group Theory

## Is abelian group $G$ always isomorphic to H×(G/H)?

Let and Then .We know is cyclic. Cayley Table of is:       And . Cayley Table of is: Then, . So, the group structures of are Isomorphic.That is . And . is Identity in . Cayley Table of is: The Group structure of is Isomorphic to :   Therefore,  is not isomorphic to . Share This:

## Group homomorphism and examples

Group A group is any set G with a defined binary operation (called the group law of ), written as 2 tuple (examples: ), satisfying 4 basic rules Closure The important point to be understood about a binary operation on is that is closed with respect to in the sense that if then ( can be read as "a,b element of C" or "a,b in C") Associativity   ( can...

## A Day out with FreePlane Mindmap and Mathematical Groups

Background I wanted to break away from Blender Learning/Modeling (Current passion) for a day or two. And so I began my exploration in Mathematical Groups using FreePlane Mind mapping software. I had recently switched from Freemind to to Freeplane. There was a simple enough reason for this decision - LaTeX support. Freeplane allows us to enter Mathematical equations using LaTeX. But a certain disadvantage of using Freeplane is that you...