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Math Help - Abelian and Cyclic groups

  1. #1
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    Abelian and Cyclic groups

    Another Group theory question - sorry! Any help greatly appreciated...
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  2. #2
    MHF Contributor kalagota's Avatar
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    try doing it by force. it has only 8 elements as they say..
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  3. #3
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    What method do I use for this?
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  4. #4
    MHF Contributor kalagota's Avatar
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    you already have A and B initial elements..

    now, how will you get other elements? try solving for AB, BA, AA, BB..
    if you obtain other elements other than the identity, A and B, try multiplying it with either A or B to obtain another elements..
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  5. #5
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    Thanks, so would i try the following to confirm:

    AA
    AB
    BA
    BB
    ABA
    BAA
    AAB
    BBA

    and the answers that dont give A or B or e are the non identity elements (in product form)
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  6. #6
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    Thanks

    What about (iii)? Any help greatfully received
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