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Affine Completeness of Generalised Dihedral Groups

Open Access article
 Printed: Sep 2006
  • J├╝rgen Ecker
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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, 16Y30, 20F05 show english descriptions Operations, polynomials, primal algebras
Near-rings [See also 12K05]
Generators, relations, and presentations
08A40 - Operations, polynomials, primal algebras
16Y30 - Near-rings [See also 12K05]
20F05 - Generators, relations, and presentations

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