Geodesic
Remarks on Quasigroups Obeying a Generalized Associative Law
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 17-21

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T. Evans in [4] introduced a concept generalizing the associative law for groups. Certain very restricted cases of this generalization had occurred, somewhat as side results, in the considerations of A. K. Suškevič [7], D. C. Murdoch [5], [6], and R. H. Bruck [2] associated with quasigroups which obey theorems generalizing certain results in group theory.In this paper we consider quasigroups obeying an instance of Evans' generalization. We show two means of constructing such quasigroups, and we demonstrate these constructions with several examples. The principal result of this paper is a theorem which reveals a peculiar trait of quasigroups obeying an instance of the generalized associative law we are considering. Such a quasigroup obeys a law expressed with permutations in which the nontrivial permutations involved either are both automorphisms of the quasigroup or else both fail to distribute over any product from the quasigroup. 
Remarks on Quasigroups Obeying a Generalized Associative Law. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 17-21. doi: 10.4153/CMB-1970-004-7
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     journal = {Canadian mathematical bulletin},
     pages = {17--21},
     year = {1970},
     volume = {13},
     number = {1},
     doi = {10.4153/CMB-1970-004-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-004-7/}
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