Determining semidirect product

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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 <sigma>

Show that the dihedral group D_n=<a,b|a^n=b^2=1,b^-1ab=a^-1> is a semidirect product of A=<a> by B=<b>

Show that the quaternion group Q_2 cannot be expressed as a semidirect product of two non-trivial subgroups.

Reference no: EM13124528

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