ON THE IDENTITIES OF BOL-MOUFANG TYPE

In this work we study properties of five identities of Bol-Moufang type (1). We establish a necessary and sufficient condition for a loop to be an RC-loop. A corollary to this is the condition for a Bol loop to be an RC-loop. Some proerties of a generalization of RC-loops are discussed. We also state the relationship between the supernucleus M(G) of a loop G and the nucleii of loops which do not have the inverse property. Finally, we give two tables of non-associative RC-loops of order 16, which are not Bol loops.