The word problem for κ-terms over the pseudovariety of local groups

Abstract

In this paper we study the κ-word problem for the pseudovariety LG of local groups, where κ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary κ-term α into another one α* called the LG-canonical form of α and by showing that different canonical forms have different interpretations over LG. The procedure of construction of these canonical forms consists in applying reductions determined by a set ∑ of κ-identities. As a consequence, ∑ is a basis of κ-identities for the κ-variety generated by LG.