English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A prefix monoid is a finitely generated submonoid of a finitely presentedgroup generated by the prefixes of its defining relators. Important results ofGuba (1997), and of Ivanov, Margolis and Meakin (2001), show how the wordproblem for certain one-relator monoids, and inverse monoids, can be reduced tosolving the membership problem in prefix monoids of certain one-relator groups.Motivated by this, in this paper we study the class of prefix monoids offinitely presented groups. We obtain a complete description of this class ofmonoids. All monoids in this family are finitely generated, recursivelypresented and group-embeddable. Our results show that not every finitelygenerated recursively presented group-embeddable monoid is a prefix monoid, butfor every such monoid if we take a free product with a suitably chosen freemonoid of finite rank, then we do obtain a prefix monoid. Conversely we provethat every prefix monoid arises in this way. Also, we show that the groups thatarise as groups of units of prefix monoids are precisely the finitely generatedrecursively presented groups, while the groups that arise as Sch\"utzenbergergroups of prefix monoids are exactly the recursively enumerable subgroups offinitely presented groups. We obtain an analogous result classifying theSch\"utzenberger groups of monoids of right units of special inverse monoids.We also give some examples of right cancellative monoids arising as monoids ofright units of finitely presented special inverse monoids, and show that notall right cancellative recursively presented monoids belong to this class.

Prefix monoids of groups and right units of special inverse monoids