Normal subgroup|important theorems

H is normal subgroup iff product of two right coset is again a right coset

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prove that centre Z(G) of a group is a normal subgroup of group G BSc part 3 math honours #tmbu

2 nd bsc mathematics, If H,K are subgroups of G Hk is subgroup of G iff Hk=kH

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(Question:4)If H is a subgroup of a group G and g€G then prove that gHg^-1 is a subgroup of G.

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(Corollary:2) The order of every element of a finite group is divisor of the order of the group.

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Group Theory | Normal Subgroup | Simple Group | Invariant Subgroup | Abstract Algebra

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