Wallpaper Groups and the Pòlya Enumeration Theorem
Arvid Börtz · 2014
The main purpose of this thesis is to present the seventeen classes of wallpaper groups. These are certain subgroups of the isometries of the plane, that preserve lattices. The concept of semidirect product will be introduced, since most of the wallpaper groups are constructed with this product, which is a generalization of the ordinary direct product of groups. Finally there is a part on the Polya Enumeration Theorem, which is a kind of generalization of Burnside's Lemma, that will provide more detailed information about the objects being investigated.