Exotic groups and quotients of loop groups

A study is made of various category-theoretic properties of exotic groups. Exotic groups that are non-commutative and non-metrizable are constructed for the first time. A proof is given of a theorem on the construction of exotic groups by means of groups of continuous maps (or maps of smoothness $r<\infty$) from a real complete space (respectively, a locally compact manifold) to a locally compact group (respectively, a Lie group) via factorization. It is shown that quotients of loop groups or generalized loop groups with respect to their closed normal subgroups are either commutative exotic groups, or else non-exotic groups.