Let $\displaystyle X=S_n$ and $\displaystyle x \in K=\cap_{g \in X}H^g$

Then

(1) $\displaystyle \mid X: K \mid \geq \mid X: H \mid =n$, where H is a subgroup of X.

(2) As $\displaystyle n\geq 3, K=1.$

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- Aug 11th 2008, 01:34 AMdimukhelp...
Let $\displaystyle X=S_n$ and $\displaystyle x \in K=\cap_{g \in X}H^g$

Then

(1) $\displaystyle \mid X: K \mid \geq \mid X: H \mid =n$, where H is a subgroup of X.

(2) As $\displaystyle n\geq 3, K=1.$