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Math Help - wreath product of groups

  1. #1
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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. #2
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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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    Thank you !
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