let f be homomorphism and if H is Abelian then f(H) is Abelian

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If f: G→H is a surjective homomorphism oh groups and G is abelian, prove that H is abelian. If f: G→H is a surjective homomorphism oh groups and G is abelian, prove that H is abelian.
Theorem: if Phi is a homomorphism from G ONTO G Theorem: if Phi is a homomorphism from G ONTO G'.if G is abelian then G' is also abelian
let f be homomorphism and if H is cyclic then f(H) is cyclic let f be homomorphism and if H is cyclic then f(H) is cyclic
Lec-7 Let H be an Abelian subgroup of a group G.If f:G→H is any into homomorphism then  G Lec-7 Let H be an Abelian subgroup of a group G.If f:G→H is any into homomorphism then  G'⊂ker f
Every homomorphic image of an Abelian group is abelian. Every homomorphic image of an Abelian group is abelian.
Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism
If in a group G * a ^ 5 = e aba^-1= b^2 for a, b belongs to G then show that o(b) = 31 If in a group G * a ^ 5 = e aba^-1= b^2 for a, b belongs to G then show that o(b) = 31
If G is Abelian then G If G is Abelian then G' is also Abelian