Representations of n-cyclic groupoids (Q1118705)

An n-cyclic groupoid is a groupoid satisfying the following four identities: \((xy)z=(xz)y\), \(xx=x\), \(x(yz)=xy\), \((((xy)y)...)y=x\) where y is repeated n times. A decomposition of an n-cyclic groupoid into a disjoint sum of abelian groups is found and the result is applied to describe free objects, to establish properties of congruence relations and to characterize subdirectly irreducible groupoids in the variety of n-cyclic groupoids.