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Math Help - Problem in group theory

  1. #1
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    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.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Problem in group theory

    Quote Originally Posted by lilymuka View Post
    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?
    How about other combinations?
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  3. #3
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    Re: Problem in group theory

    Quote Originally Posted by ILikeSerena View Post
    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?
    How about other combinations?
    Thanks a lot! I am following your lead!
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