Finite left distributive algebras with one generator (Q1373278)

The paper initiates the study of finite monogenerated left self-distributive groupoids (i.e., groupoids satisfying \(x\cdot yz=xy\cdot xz\)). Many technical results (which should hopefully lead to a complete description of the groupoids mentioned) are proven. Among others, the monogenerated groupoids are shown to be closely related to the well-known groupoids \(A_k(*)\) defined on \(\{1,\dots,2^k\}\) by \(a*1\equiv a+1\bmod{2^k}\).