If G is a group such that (ab)= a^{2}b^{2}forevery a,b Є G, show that G is abelian.

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- Mar 17th 2014, 02:45 AMAman3230show that G is abelian....
If G is a group such that (ab)= a

^{2}b^{2}forevery a,b Є G, show that G is abelian. - Mar 17th 2014, 04:56 AMFernandoRevillaRe: show that G is abelian....
- Mar 17th 2014, 05:20 AMAman3230Re: show that G is abelian....
thanks 4 reply.....

in my text book only (ab)= a2b2 was given anyway

thanks alot 4 giving ur precious time - Mar 17th 2014, 05:35 AMDevenoRe: show that G is abelian....
If ab = a

^{2}b^{2}for every a,b in G, then it certainly is the case for a = e, the identity of G.

Then we have:

eb = e^{2}b^{2}

b = b^{2}

e = b, for EVERY b in G, which means that G is a group with only one element: e. - Mar 17th 2014, 05:41 AMAman3230Re: show that G is abelian....
thanks