Geodesic
Commutators and associators in Catalan loops
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 333-347 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops.
Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops.
Classification : 20F12, 20N05
Keywords: loop; right loop; left loop; commutator; associator 
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     author = {Raasch, Jan M.},
     title = {Commutators and associators in {Catalan} loops},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {333--347},
     year = {2010},
     volume = {51},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a16/}
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Raasch, Jan M. Commutators and associators in Catalan loops. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 333-347. http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a16/