If G is a group, and a,b are in G, and e=aba^{3}b^{2}a prove that G is trivial. I am stucked.

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- Apr 11th 2013, 07:05 PMlilymukaProblem in group theory
If G is a group, and a,b are in G, and e=aba

^{3}b^{2}a prove that G is trivial. I am stucked. - Apr 13th 2013, 05:11 AMILikeSerenaRe: Problem in group theory
Hi lilymuka! :)

I'm reading your statement as: for any a,b in G we have e=aba^{3}b^{2}a.

Otherwise your problem makes no sense.

Now suppose G is not trivial.

Then there is at least some c in G, which is distinct from e.

What do you get if you fill in c for a and e for b?

How about other combinations? - Apr 13th 2013, 06:44 AMlilymukaRe: Problem in group theory