Abstract: Based on the structure of the quasidihedral 2-group and the properties of its elements in group theory, we used the basic method in algebra to construct all homomorphisms from two different the quasidihedral 2-groups. We also got the result that conjecture of Asai and Yoshida was satisfied on the quasi-dihedral 2-group.

Key words: quasi-dihedral 2-group, commutator subgroup, homomorphism