What is Group theory?

Any mathematical endeavor starts with a set of assumptions/axioms/rules to define the boundaries of mathematical object being studied. In Group theory, a Group is a set of actions that abide by below rules:

  1. There is a predefined list of actions that never changes.(generators)
  2. Every action is reversible.
  3. Every action is deterministic.
  4. Any sequence of consecutive actions is also an action

 

Sub group is a group that exists inside a group. We generally write it as B<A.

Normal subgroup is a subgroup who’s all left cosets are equal to it’s right cosets.

Normalizers of subgroup H which is not normal in Group G is NhG which represents set of all generators whose left coset of H is equal to right coset of H.

Isomorphism is special case of Homomorphism

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