Prove that, if H is a subgroup of a cyclic group G, then the quotient group G/H is also cyclic.
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- Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.Assume that G is a finite group, and let H be a nonempty subset of G. Prove that H is closed if and only if H is subgroup of G.True or False Label each of the following statements as either true or false. 4. If a subgroup of a group is cyclic, then must be cyclic.