Affine completeness of generalised dihedral groups

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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 ∈ 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.

Original languageEnglish
Pages (from-to)347-357
Number of pages11
JournalCANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
Volume49
Issue number3
DOIs
Publication statusPublished - Sep 2006

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