Q5Discrete Mathematics Structure

Question

Define the following : (i) Permutation groups (ii) Normal subgroup (iii) Homomorphism group (iv) Isomorphism group

Answer 1

(i) Permutation groups: A group whose elements are permutations of a given set and whose group operation is the composition of permutations.
(ii) Normal subgroup: A subgroup $H$ of $G$ is normal if for every $g \in G$ , $g H g^{- 1} = H$ .
(iii) Homomorphism group: A mapping between two groups that preserves the group operation.
(iv) Isomorphism group: A bijective homomorphism between two groups.

Question