A survey of the theory of loops

This thesis consists of an up to date (June, 1956) survey of the theory of loops. The arrangement of the material is as follows. Chapter 1 starts with a discussion of permutation groups, Quasigroups are then defined, and we see that a quasigroup can be considered to consist of a set G of elements and an associated set of permutations of these elements. Loops are next defined as quasigroups with an identity element. A discussion of the formal equivalence relation of isotopuy shows that the study of quasigroups can, within isotopy, be reduced to the study of loops. The chapter is concluded with a discussion of homomorphisms, characterstic subloops, normal subloops, quotient loops, and the inner mapping group of a loop...