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Math Help - isomoprhism

  1. #1
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    isomoprhism

    Hi,

    whcih of the following groups would be isomorphic?

    D32
    A5
    D22
    A22
    A32
    S32
    S22
    Z60
    S60
    A60.

    thanks
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  2. #2
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    Quote Originally Posted by nidak View Post
    D32
    64 elements

    A5
    60 elements.

    D22
    44 elements.

    A22
    22!/2 elements.

    A32
    32!/2 elements.

    S32
    32! elements

    S22
    22! elements.

    Z60
    60 elements.

    S60
    60! elements.

    A60.
    60!/2 elements.

    The only ones that have a chance of being isomorphic are A5 and Z60. But A5 is non-abelian and Z60 is. So there is no isomorphism here.
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  3. #3
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    more..

    C x R
    Z4 x Z3 x Z5
    D11 x Z2
    Z4 x Z8
    S22
    Z60
    A5
    A22
    A32
    S32
    A60
    S60
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  4. #4
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    Quote Originally Posted by nidak View Post
    C x R
    2^{\aleph_0}
    Z4 x Z3 x Z5
    60
    D11 x Z2
    44
    Z4 x Z8
    32
    S22
    22!
    Z60
    60
    A5
    60
    A22
    22!/2
    A32
    32!/2
    S32
    32!
    A60
    60!/2
    S60
    60!

    The only possible ones are:
    Z4xZ3xZ5 and Z60 and A5
    We note the first two are abelian and third one is not.
    Thus, it remains to show that the first two are or not isomorphic.

    Indeed they are because 4,3,5 in Z4xZ3xZ5 are relatively prime.
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