20. If G is abelian then (ab)^n=a^nb^n, for all a,b in G (Proof by mathematical induction)

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If G is Abelian, Prove (ab)^n=(a^n)(b^n) ∀ positive n ∈ ℤ & ∀ a, b ∈ G If G is Abelian, Prove (ab)^n=(a^n)(b^n) ∀ positive n ∈ ℤ & ∀ a, b ∈ G
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)^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
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.
If G is an abelian group, then for a, b in G and all integers, n, (ab)^n = a^nb^n. |. If G is an abelian group, then for a, b in G and all integers, n, (ab)^n = a^nb^n. |.
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
example group :-If a, b are elements of abelian group G then prove, (ab)^n =a^nb^n , n belongs to Z example group :-If a, b are elements of abelian group G then prove, (ab)^n =a^nb^n , n belongs to Z
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.