Benard M. Kivunge, Jonathan D. H Smith (2004)
Commentationes Mathematicae Universitatis Carolinae
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This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.
Mark Greer, Lee Raney (2014)
Commentationes Mathematicae Universitatis Carolinae
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We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms,...
Orin Chein, Edgar G. Goodaire (2002)
Commentationes Mathematicae Universitatis Carolinae
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We investigate finite Moufang loops with a unique nonidentity commutator which are not associative, but all of whose proper subloops are associative. Curiously, perhaps, such loops turn out to be ``ring alternative'', in the sense that their loop rings are alternative rings.