Problem in group theory

• Apr 11th 2013, 06:05 PM
lilymuka
Problem in group theory
If G is a group, and a,b are in G, and e=aba3b2a prove that G is trivial. I am stucked.
• Apr 13th 2013, 04:11 AM
ILikeSerena
Re: Problem in group theory
Quote:

Originally Posted by lilymuka
If G is a group, and a,b are in G, and e=aba3b2a prove that G is trivial. I am stucked.

Hi lilymuka! :)

I'm reading your statement as: for any a,b in G we have e=aba3b2a.
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?
• Apr 13th 2013, 05:44 AM
lilymuka
Re: Problem in group theory
Quote:

Originally Posted by ILikeSerena
Hi lilymuka! :)

I'm reading your statement as: for any a,b in G we have e=aba3b2a.
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?