A Development of the Loop Concept
Abstract
The purpose of this thesis is to present in as lucid a manner as possible, the various properties of the abstract
binary system defined as a loop. Special emphasis will be
placed on the comparative development of other binary systems
with the development of loop theory. Whenever possible, analogous
theorems and lemmas will be explored in each system, and
the necessary changes, both in the proofs and in the theorems
themselves, will be particularly noted. The first section of
the paper will investigate two generalizations of a loop,
groupoids and quasi-groups, and properties will be developed
that are particularly relevant to loop theory. In the second
section, loops will be discussed in relation to groups; a loop
is itself a generalization of a group.