Loops that are partitioned by groups

Abstract

AbstractA set of subgroups of a group is said to be a partition if every nonidentity element belongs to one and only one subgroup in this set. The study of groups with partition dates back to a paper by Miller published in 1906 ([Bull. Amer. Math. Soc. 17 (1906/1907), 446–449]). In this paper we study the structure of loops that are partitioned by subgroups.