On loops covered by subloops

The topic of this paper is the investigation of coverings of a loop by subloops. A loop has a covering by subloops if it is the set-theoretic union of proper subloops. If the set of subloops is finite, the covering is called finite. Coverings of groups by subgroups have been widely investigated and key results are detailed in the introduction. Various analogues for loops of the results for groups are obtained. An example of an infinite loop which is the union of three proper commutative subloops, but has no finite homomorphic images and has a trivial center, shows that the results for loops cannot be as general as for groups, justifying additional assumptions on the loops or the coverings.