Normal subgroup theorems exmaples Group theory

Normal subgroup theorems exmaples Group theory
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#grouotheory
#normalsubgroup
Group Theory Normal Subgroup Simple Group Hamiltonian Abstract Algebra properties Theorems
1. Normal subgroup
2. Definition of normal subgroup
3. Proper and improper normal subgroup
4. Simple subgroup
5. Hamiltonian
6. Properties of normal subgroup
1. Every subgroup of an abelian group is normal subgroup
2. A subgroup h of a group G is a normal subgroup if and only if xHx1=H
3. A subgroup H of group G is a normal subgroup if and only if each left is set of right concept of H
4. A subgroup H of a group G is a normal subgroup of G if and only if the product of two right cosets of H in is again a right cosets of H i n G
5. theorems on normal subgroup
The intersection of any two normal subgroup of group is a normal subgroup
All theorems of normal sub group
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