Towards a geometric theory for left loops

Commentationes mathematicae Universitatis Carolinae

Karla Baez¹ 

关键词: left loops;    Cayley graphs;    rate of growth;    hyperbolicity;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

In [Mwambene E., {\it Multiples of left loops and vertex-transitive graphs\/}, Cent. Eur. J. Math. {\bf 3} (2005), no.~2, 254--250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.

【 授权许可】

CC BY