Finite Presentability of Brin-Higman-Thompson Monoids via Free Jónsson-Tarski Algebras

Abstract: We show that the total monoids totnM_{k,1} introduced by Birget(and their multi-rooted generalisations), which extend the Brin-Higman-Thompson groups, can be realised as the endomorphism monoids of higher dimensional J\'onnson-Tarski algebras. We use this representation to show that they are finitely presented.