Abstract:

Let G be a semidirect product of a finite abelian group A and a dihedral group D of order 2n, where each element of D acts on A by raising every element of A to some fixed power. Suppose that a Sylow 2-subgroup of G has an abelian subgroup of index 2. Then Out_c(G)=1. In particular, the normalizer property holds for such a group G.

Key words: class-preserving automorphisms; normalizer property; integral group rings