IMI/Publicaţii/QRS/Ediţii/QRS v.21, n.1 (29), 2013/

Nuclei and commutants of C-loops

Authors: M. Shah, A. Ali and V. Sorge


C-loops are loops that satisfy the identity x(y(yz))=((xy)y)z. In this note we use the order of nuclei of C-loops to show that (1) nonassociative C-loops of order 2p, where p is prime, are Steiner loops, (2) nonassociative C-loops of order 3n are non-simple and non-Steiner, (3) no nonassociative C-loop of order 2(3t) exists, and (4) if every element of the commutant of a C-loop is of odd order the commutant forms a subloop.


Adobe PDF document0.20 Mb