Knowledge in Group theory
Inner and Outer Automorphism
Two types of automorphism i.e. inner and outer automorphism.... Theorem that set of all inner automorphism is a normal Subgroup and two more theorems that phi is automorphism iff G is abelian
Ishant Goel
Commutator of a group
Definition of commutator of a group and it's theorem and definition of derive group, it's another name is commutative subgroup and it's theorem
Direct product of groups
Definition of direct product of groups, in the direct product, every element of H is commute with every element of K and every element of G is uniquely expressible And more results too
Invariant and characteristic subgroup
If G is a group and G=H×K, then the factor group G/K is isomorphic to H.... Another result that if H and K are cyclic groups then H×K is a cyclic group.... Definition and examples of invariant and characteristic subgroup