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On some systems of equations with constraints in a free group. – Addenda. (Sur certains systèmes d’équations avec constraintes dans un groupe libre. – Addenda.) (French) Zbl 1046.20023
This paper is a complement of a previous paper of the authors [Port. Math. 56, No. 4, 409-417 (1999; Zbl 0960.20014)]. In the present paper they correct a mistake made in the above mentioned paper but also clarify the situation. The main result of this paper is to show that the theorem of C. J. Ash [Int. J. Algebra Comput. 1, No. 1, 127-146 (1991; Zbl 0722.20039)] applied in the case of inversive monoids implies the result of B. Herwig and D. Lascar (Theorem 5.1) in [Trans. Am. Math. Soc. 352, No. 5, 1985-2021 (2000; Zbl 0947.20018)].

MSC:
20E05 Free nonabelian groups
20E10 Quasivarieties and varieties of groups
20M07 Varieties and pseudovarieties of semigroups
20E18 Limits, profinite groups
20E07 Subgroup theorems; subgroup growth
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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