VARIETIES OF P-QUASIGROUPS

Decompositions of complete undirected graphs into sets of closed trails which partition the edge set of the graph and which contain each pair of distinct vertices exactly once at distance 2 define and are defined by a class of quasigroups called P-quasigroups. Conditions are established under which P-quasigroups are (or are not) homomorphic images of P-quasigroups which possess certain properties. The variety generated by the class of quasigroups arising from all 2-perfect m-cycle systems (uniform m-P-quasigroups) is thereby determined for all positive integers m, (m =J. 1,2 or 4). An equational basis is given for each such variety