Relatives of K-loops: Theory and examples

Abstract

summary:A {\it K-loop\/} or {\it Bruck loop\/} is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of {\it derivation\/} is introduced. This has been used in the past to construct quasifields from fields. Many known methods to constructing loops can be seen as special cases of derivations. The examples given show the independence of various axioms