1. CMB 2006 (vol 49 pp. 347)
|Affine Completeness of Generalised Dihedral Groups |
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.
Categories:08A40, 16Y30, 20F05