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Thread: wreath product of groups

  1. #1
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    Question wreath product of groups

    Is $\displaystyle S_m \wr S_m \ldots \wr S_m$ (n times) $\displaystyle \cong S_{m^n}$ ? , where $\displaystyle \wr$ 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 $\displaystyle

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

    plz explain.
    no! compare the orders. for example for $\displaystyle m>1$ and $\displaystyle n=2$ we have $\displaystyle |S_m \wr S_m|=(m!)^{m+1} \neq (m^2)! =|S_{m^2}|.$
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    Thank you !
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