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# Affine Completeness of Generalised Dihedral Groups

Published:2006-09-01
Printed: Sep 2006
• Jürgen Ecker
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## Abstract

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.
 MSC Classifications: 08A40 - Operations, polynomials, primal algebras 16Y30 - Near-rings [See also 12K05] 20F05 - Generators, relations, and presentations