Theorem 7| if (ab)^i= a^i b^i for three consecutive integers then G is Abelian| | B.Sc, JAM, CSIR

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(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. |
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.
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
Theorem for abelian group- 3rd B.Sc Mathematics Theorem for abelian group- 3rd B.Sc Mathematics
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If a+b=7 & a²−b²=21, Find a−b ✨ | O-Level Algebra Trick If a+b=7 & a²−b²=21, Find a−b ✨ | O-Level Algebra Trick
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.