Medial and Semimedial Left Quasigroups

In this paper, we investigate the class of semimedial left quasigroups, a class that properly contains racks and medial left quasigroups. We extend most of the results about commutator theory for racks collected in [M. Bonatto and D. Stanovský, Commutator theory for racks and quandles, preprint (2019), arXiv:1902.08980 .] and we provide a structure theorem for finite medial connected racks.