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:
- There is a predefined list of actions that never changes.(generators)
- Every action is reversible.
- Every action is deterministic.
- 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