Normal and characteristic structure in quasigroups and loops
thesisposted on 15.12.2014 by Tim. Hardcastle
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
In this thesis I shall be exploring the normal and characteristic structure of quasigroups and loops. In recent years there has been a revival of interest in the theory of loops and in particular in the relationship between the properties of a loop and the properties of its multiplication group; and several powerful new theorems have emerged which allow the structural properties of a loop to be related to its multiplication group. I shall combine these ideas with tools developed at the beginning of loop theory to produce some interesting new theorems, principally relating the order of a finite multiplication group to the structure of its loop.