2023/05/27 by Inam, Muhammad
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2305.17312
We introduce the notion of a subgraph generated by an R-word r of the Schützenberger graph of a positive word w, SΓ(w), where w contains r as its subword. We show that the word problem for a finitely presented Adian inverse semigroup Inv⟨ X|R ⟩ is decidable if the subgraphs of SΓ(t), for all t∈ X+, generated by all the R-words over the presentation ⟨ X|R⟩, are finite. As a consequence of this result, we show that the word problem is decidable for some classes of one relation Adian inverse semigroups.