showing the group is abelian

Asked May 04 '14 at 16:47

Active May 04 '14 at 16:58

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I need someone to guide me to solve the following problem

Let $a, b \in G$.
a. f $(a *b)^i = a^i * b^i$ for three consecutive natural numbers, then show that $G$ is Abelian.
b. If the above property holds only for two numbers, then it is not necessarily Abelian.

edited May 04 '14 at 16:58

asked May 04 '14 at 16:47

Mula Ko Saag

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What do you mean by three consecutive integers? – May 04 '14 at 16:51
@SanathDevalapurkar sorry, should have mentioned for natural numbers. $i, i+1, i+2$ – Mula Ko Saag May 04 '14 at 16:53
$$(ab)^i=ababab\cdotsab=aaa*\cdotsabbb\cdotsb*b$$Can you see it now? – May 04 '14 at 16:54
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@NajibIdrissi yes that is the question also from the same book except that I added the another following problem. – Mula Ko Saag May 04 '14 at 16:57

showing the group is abelian

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