Abstract.  

Q, • is a quasigroup if • : QxQ → Q such that the equations:
a•x = b, y•a = b
have unique solutions in Q for all a,b in Q. L,• is a loop if L,• is a
quasigroup with identity. So, informally, a loop is non-associative
group. Historically, loops arose in the study of non-associative algebras
and the search for non-desarguesian geometries. In this talk, we will
survey how groups are used to study loops.