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Affine Completeness of Generalised Dihedral Groups

Published online by Cambridge University Press:  20 November 2018

Jürgen Ecker
Jürgen Ecker*
Affiliation:
Institut für Algebra, Johannes Kepler Universität Linz, 4040 Linz, Austria and Computer- und Mediensicherheit, FH Oö Campus Hagenberg, 4232 Hagenberg, Austria e-mail: juergen.ecker@fh-hagenberg.at
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Abstract

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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 $k\in \mathbb{N}$ 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.

Keywords

08A4016Y3020F05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 3 , 01 September 2006 , pp. 347 - 357
Copyright
Copyright © Canadian Mathematical Society 2006

References

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