Normal subgroup

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May 4th 2010, 08:34 AM
cvcv49

Normal subgroup

An Normal subgroup of Sn?
why??
May 4th 2010, 08:37 AM
tonio

Quote:

Originally Posted by cvcv49

An Normal subgroup of Sn?
why??

Proof 1: because $[S_n:A_n]=2$ ;

Proof 2: because $\pi^{-1}\sigma\pi\in A_n\,\,\,\forall\,\pi\in S_n\,\,\forall \sigma\in A_n$

Tonio
May 6th 2010, 07:36 AM
FancyMouse

And also a trivial one and $S_n$ itself

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