International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 3, Pages 181-187

Loops embedded in generalized Cayley algebras of dimension 2r,r2

Raoul E. Cawagas

SciTech Center, Polytechnic University of the Philippines, Manila, Philippines

Received 9 August 2000; Revised 19 March 2001

Copyright © 2001 Raoul E. Cawagas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Every Cayley algebra of dimension 2r,r2, contains an embedded invertible loop of order 2r+1 generated by its basis. Such a loop belongs to a class of non-abelian invertible loops that are flexible and power-associative.