If (ab)^n=a^nb^n for three consective integer n, where a,b€G then G is Abelian |Group theory | Hindi

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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
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
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)
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.
(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. |
in a group G (ab)^n=a^nb^n for there consecutive integers then G is abelian in a group G (ab)^n=a^nb^n for there consecutive integers then G is abelian
If G is an abelian group then show that (ab) ^n=a^nb^n. If G is an abelian group then show that (ab) ^n=a^nb^n.