Displaying similar documents to “The inner mappings of extra loops”

Bol loops with a large left nucleus

Orin Chein, Edgar G. Goodaire (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Possession of a unique nonidentity commutator/associator is a property which dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an ``interesting'' identity. Indeed, until now, with the exception of some ad hoc examples, the only known class of Bol loops whose loop rings satisfy the right Bol identity have this property. In this paper, we identify another class of loops whose loop rings are ``strongly right alternative'' and present various constructions...

When is it hard to show that a quasigroup is a loop?

Anthony Donald Keedwell (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We contrast the simple proof that a quasigroup which satisfies the Moufang identity ( x · y z ) x = x y · z x is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity ( x y · z ) y = x ( y · z y ) is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.