If (ab)^i=a^ib^i for 3 consecutive integers i, then prove that the group is abelian. #abeliangroup

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(ab)^i = a^i*b^i for 3 consecutive integers G is abelian. | (ab)^i = a^i*b^i for 3 consecutive integers G is abelian. |
(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 (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.
Theorem 7| if (ab)^i= a^i b^i for three consecutive integers then G is Abelian| | B.Sc, JAM, CSIR Theorem 7| if (ab)^i= a^i b^i for three consecutive integers then G is Abelian| | B.Sc, JAM, CSIR
19. If for three consecutive natural numbers (ab)^n=a^nb^n then G is abelian 19. If for three consecutive natural numbers (ab)^n=a^nb^n then G is abelian
If (ab)^3 = a^3b^3 for all a, b in G, then G is abelian . If (ab)^3 = a^3b^3 for all a, b in G, then G is abelian .
If (ab)^n=a^n b^n for three consective integers n where a,b €G then G is abelian||theorem||group T If (ab)^n=a^n b^n for three consective integers n where a,b €G then G is abelian||theorem||group T
Theorem for abelian group- 3rd B.Sc Mathematics Theorem for abelian group- 3rd B.Sc Mathematics