If G is a group, and a,b are in G, and e=aba3b2a prove that G is trivial. I am stucked.
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?
How about other combinations?