internal semi-direct product with homomorphism
Let H be a cyclic group under addition. Let q=internal semidirect product between Zn and Z2. Let f: H to H be the inversion automorphism defined byf(x)=-x. Define a: Z2 to Aut(H) to be the homomorphism that maps a(1)=f. Show Zn qa Z2 is isomorphic to Dn by identifying two generators in Zn qa Z2 that satisfy the relations for Dn.
Note: (1) f is an element of Aut(H) and a is a well-defined homomorphism since f is an order 2 element of Aut(h).
(2) If H=Z, then Z qa Z2 is isomorphic to the infinite dihedral group.
I really have no idea how to find the generators in Zn qa Z2, anyhelp on this would be great!!!