if G Is a group such that (ab)^n=a^n.b^n for three consecutive integers n for all a,b in G, Show tha

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Show that G is abelian if for all a, b in G, (ab) ^n=a^nb^n for three consecutive natural numbers.Show that G is abelian if for all a, b in G, (ab) ^n=a^nb^n for three consecutive natural numbers.
(ab)^i=a^i.b^i for three consecutive integers of i, then show G is abelian.(ab)^i=a^i.b^i for three consecutive integers of i, then show G is abelian.
If in a group G * a ^ 5 = e aba^-1= b^2 for a, b belongs to G then show that o(b) = 31If in a group G * a ^ 5 = e aba^-1= b^2 for a, b belongs to G then show that o(b) = 31
If (ab)^n=a^n b^n for three consective integers n where a,b €G then G is abelian||theorem||group TIf (ab)^n=a^n b^n for three consective integers n where a,b €G then G is abelian||theorem||group T
20. If G is abelian then (ab)^n=a^nb^n, for all a,b in G (Proof by mathematical induction)20. If G is abelian then (ab)^n=a^nb^n, for all a,b in G (Proof by mathematical induction)
in a group G (ab)^n=a^nb^n for there consecutive integers then G is abelianin a group G (ab)^n=a^nb^n for there consecutive integers then G is abelian
19. If for three consecutive natural numbers (ab)^n=a^nb^n then G is abelian19. If for three consecutive natural numbers (ab)^n=a^nb^n then G is abelian
If (ab)^i=a^i b^i ∀ a,b∈G for three consecutive integers i, then G is abelian.If (ab)^i=a^i b^i ∀ a,b∈G for three consecutive integers i, then G is abelian.