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- Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19:
- Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?If H and K are arbitrary subgroups of G, prove that HK=KH if and only if HK is a subgroup of G.Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.