Mathematics, Department of


Date of this Version

Summer 7-2016


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy Major: Mathematics Under the Supervision of Professor Mark Brittenham and Professor John Meakin, Lincoln, Nebraska July, 2016


The class of Adian semigroups and Adian groups was first introduced and studied by S. I. Adian in 1966. We introduce the notion of Adian inverse semigroups with the hope that the study of these objects may help in resolving some of the remaining open questions about Adian semigroups and Adian groups. We first prove that Adian inverse semigroups are E-unitary. We then prove that if is a finitely presented Adian inverse semigroup which satisfies the property that the Schützenberger complex of each positive word X+ over the presentation is finite, then the Schützenberger complex of every word over the presentation is finite. As a consequence of this result we are able to solve the word problem for some classes of Adian inverse semigroups, Adian semigroups and Adian groups.

Advisors: Mark Brittenham and John Meakin