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Abstract
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International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 3, Pages 181-187
doi:10.1155/S0161171201010766

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

Raoul E. Cawagas

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

Received 9 August 2000; Revised 19 March 2001

Abstract

Every Cayley algebra of dimension 2r,r≥2, 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.