Example
A
n
in S
n
SL
n
(
R
) in GL
n
(
R
)
A
n
is the kernel of sgn.
The subgroup SL
n
(
R
) is normal in GL
n
(
R
). It is the kernel of the determinant map.
An in Sn
SLn(R) in GLn(R)
An in Sn
SLn(R) in GLn(R)