The word problem for some classes of Adian inverse semigroups
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We show that all of the Schützenberger complexes of an Adian inverse semigroup are finite if the Schützenberger complex of every positive word is finite. This enables us to solve the word problem for certain classes of Adian inverse semigroups (and hence for the corresponding Adian semigroups and Adian groups).
KeywordsInverse semigroups Positive presentation Cycle free presentation Baumslag-Solitar presentation
The author of this paper is thankful to John Meakin and Robert Ruyle for their several useful suggestions.
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