The module theory of semisymmetric quasigroups, totally symmetric quasigroups, and triple systems

Branched covers induced by semisymmetric quasigroup homomorphisms

“…Semisymmetric quasigroups are among the more well-studied classes of quasigroup, in part because of their parastrophic symmetry and significance in regard to quasigroup homotopisms [17] [28], as well as their connection to combinatorial design theory [7] [16] and discrete geometry [23] [29]. In the author's previous work [19], it was established that finite semisymmetric quasigroups are in bijection with objects we refer to as alignments on polyhedra or simply alignments, which represent mappings between abstract polytopes (a combinatorial generalization of the more familiar geometric polytopes) and directed graphs.…”