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Math Help - Abstract algebra homework problem

  1. #1
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    Abstract algebra homework problem

    Hi,

    I need some urgent help with this one please:

    Let G be the set {a,b,c}.
    Construct the Cayley table for all possible operations on g such that G with each of the defined operations is a group with b as identity. How many such operation exist? Are any of the resulting groups non-Abelian?

    Any tips/advice would be much appreciated.

    Regards
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  2. #2
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    Quote Originally Posted by jackiemoon View Post
    Hi,

    I need some urgent help with this one please:

    Let G be the set {a,b,c}.
    Construct the Cayley table for all possible operations on g such that G with each of the defined operations is a group with b as identity. How many such operation exist? Are any of the resulting groups non-Abelian?

    Any tips/advice would be much appreciated.

    Regards

    See the attached immage

    Abstract algebra homework problem-capture.jpg

    To be a group each element must appear exactly once in each row and column. How many different ways can you do this.

    I hope this helps. Good luck.
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