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The computation of the commutativity degree for dihedral groups in terms of centralizers

The commutativity degree of finite groups is computed by finding the number of conjugacy classes of G. Also, finding the centralizers of a finite group can be applied to obtain the commutativity degree of the group. In this paper we construct some upper bounds for the commutativity degree in terms of centralizers for the dihedral group Dn, where the dihedral group acts on itself by conjugation.