Costa, J. C.Nogueira, C.Teixeira, M. L.2026-01-202026-01-202021-08-12Costa, J.C., Nogueira, C. & Teixeira, M.L. The word problem for k-terms over the pseudovariety of local groups. Semigroup Forum 103, 439–468 (2021). https://doi.org/10.1007/s00233-021-10207-9.0037-1912http://hdl.handle.net/10400.8/15423In 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 Σ of κ-identities. As a consequence, Σ is a basis of κ-identities for the κ-variety generated by LG.engLocal groupPseudovarietyFinite semigroupImplicit signatureWord problemκ-termCanonical formjournal article10.1007/s00233-021-10207-91432-2137