Tag: Algebra

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:

Some notes on Polynomials

(This is a work in progess...) (Note: I am doing some exploration on Galois Theory and I have written these notes on polynomials here for my own convenience. Please write in the comments section if any clarification is required. Also, I will not provide proofs here for the time being.) Some notations: The symbol is the domain of complex numbers; i.e. set of all possible complex numbers.The symbol is the domain...

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...