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Math Help - wreath product of groups

  1. January 18th 2009, 09:01 PM #1
    thippli
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    Question wreath product of groups

    Is S_m \wr S_m \ldots \wr S_m (n times) \cong S_{m^n} ? , where \wr denotes the wreath product of groups.

    plz explain.
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  2. January 19th 2009, 03:25 PM #2
    NonCommAlg
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    Quote Originally Posted by thippli View Post
    Is <br /> <br /> S_m \wr S_m \ldots \wr S_m (n times) \cong S_{m^n} ? , where \wr denotes the wreath product of groups.

    plz explain.
    no! compare the orders. for example for m>1 and n=2 we have |S_m \wr S_m|=(m!)^{m+1} \neq (m^2)! =|S_{m^2}|.
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  3. January 22nd 2009, 10:56 PM #3
    thippli
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    Thank you !
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