Affine Completeness of Generalised Dihedral Groups

http://dx.doi.org/10.4153/CMB-2006-035-8
Canad. Math. Bull. 49(2006), 347-357

  Published:2006-09-01
 Printed: Sep 2006

In this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for every $k \in~\N$ the $k$-affine complete generalised dihedral groups. We find that the direct product of a $1$-affine complete group with itself need not be $1$-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for $2$-affine completeness.