Journal Title/Source
Journal of Algebra and its Applications
Publication Date
2007
Volume
6
Page Numbers
1-20
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
C-loops are loops satisfying the identity x(y · yz) = (xy · y)z. We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleus is an abelian group. C-loops with central squares have very transparent extensions; they can be built from small blocks arising from the underlying Steiner triple system. Using these extensions, we decide for which abelian groups K and Steiner loops Q there is a nonflexible C-loop C with center K such that C/K is isomorphic to Q. We discuss possible orders of associators in C-loops. Finally, we show that the loops of signed basis elements in the standard real Cayley-Dickson algebras are C-loops.
Recommended Citation
Phillips, J.D., "C-LOOPS: EXTENSIONS AND CONSTRUCTIONS" (2007). Journal Articles. 526.
https://commons.nmu.edu/facwork_journalarticles/526