Affine Completeness of Generalised Dihedral Groups

Canadian mathematical bulletin

关键词: Euclidean buildings;    Hadamard spaces;    polygons;   

DOI  :  10.4153/CMB-2006-035-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we study affine completeness of generalised dihedralgroups. We give a formula for the number of unary compatiblefunctions on these groups, and we characterise for every $k in~N$the $k$-affine complete generalised dihedral groups. We find thatthe direct product of a $1$-affine complete group with itself need notbe $1$-affine complete. Finally, we give an example of a nonabeliansolvable affine complete group. For nilpotent groups we find astrong necessary condition for $2$-affine completeness.

【 授权许可】

Unknown