ON THE SUPERDIMENSIONS OF RELATIVELY FREE NILPOTENT SEMIGROUPS
L. M. Shneerson · International Journal of Algebra and Computation · 2004
We prove that in the variety of nilpotent semigroups of class ≤2, which is defined by the Neumann–Taylor identity xyzyx=yxzxy, the sequence of the superdimensions for relatively free semigroups is convergent to 1 and at the same time every element of the sequence is strictly less than 1. This gives the first example of a semigroup variety for which the set of superdimensions for the free objects is infinite.