Group Bijections Commuting with Inner Automorphisms

Considering the bijections of an arbitrary group  $ G $ onto itselfwhich commute with all inner automorphisms, we establish the general properties.In particular, the automorphisms constitute the group  $ B(G) $ that includes the group of central automorphisms.Also, we fully describe  $ B(D_{n}) $ for the dihedral groups  $ D_{n} $ , with $ n\in{𝕅}\cup\{\infty\} $ .