Every quotient group of an abelian group G is abelian but converse is not true.
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Every quotient group of an abelian group G
is abelian but converse is not true.
Step by step
Solved in 3 steps
- 20. If is an abelian group and the group is a homomorphic image of , prove that is abelian.25. Prove or disprove that if a group has cyclic quotient group , then must be cyclic.Let H be a torsion subgroup of an abelian group G. That is, H is the set of all elements of finite order in G. Prove that H is normal in G.