# wreath product of groups

• January 18th 2009, 09:01 PM
thippli
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.
• January 19th 2009, 03:25 PM
NonCommAlg
Quote:

Originally Posted by thippli
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.

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