If H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H.
If sigma=(12) in S_n, n>=2, show that s_n is a semidirect product of A_n by
Show that the dihedral group D_n= is a semidirect product of A= by B=
Show that the quaternion group Q_2 cannot be expressed as a semidirect product of two non-trivial subgroups.