Costa, J. C.Nogueira, C.Teixeira, M. L.2025-07-152025-07-152015-06Costa, J.C., Nogueira, C. & Teixeira, M.L. Semigroup presentations for test local groups. Semigroup Forum 90, 731–752 (2015). https://doi.org/10.1007/s00233-014-9656-20037-19121432-2137http://hdl.handle.net/10400.8/13645In this paper we exhibit a type of semigroup presentation which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety LG of all finite local groups and use them as test-semigroups to prove that LG and S, the pseudovariety of all finite semigroups, verify the same $κ-identities involving κ-terms of rank at most 1, where κ denotes the implicit signature consisting of the multiplication and the (ω-1)-power.engCanonical formLocal groupPseudovarietyRees matrix semigroupSemigroup presentationκ-termjournal article10.1007/s00233-014-9656-2