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SUMMARY:Bob Gray (East Anglia)
DTSTART:20200806T100000Z
DTEND:20200806T110000Z
DTSTAMP:20260419T060100Z
UID:CRMDS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRMDS/13/">U
 ndecidability of the word problem for one-relator inverse monoids</a>\nby 
 Bob Gray (East Anglia) as part of Western Sydney University Abend Seminars
 \n\n\nAbstract\nIt is a classical result of Magnus proved in the 1930s tha
 t the word problem is decidable for one-relator groups. This result inspir
 ed a series of investigations of the word problem in other one-relator alg
 ebraic structures. For example\, in the 1960s Shirshov proved the word pro
 blem is decidable in one-relator Lie algebras. In contrast\, it remains a 
 longstanding open problem whether the word problem is decidable for one-re
 lator monoids. An important class of algebraic structures lying in between
  monoids and groups is that of inverse monoids. In this talk I will speak 
 about a recent result which shows that there exist one-relator inverse mon
 oids of the form Inv<A|w=1> with undecidable word problem. This answers a 
 problem originally posed by Margolis\, Meakin and Stephen in 1987. I will 
 explain how this result relates to the word problem for one-relator monoid
 s\, the submonoid membership problem for one-relator groups\, and to the q
 uestion of which right-angled Artin groups arise as subgroups of one-relat
 or groups.\n
LOCATION:https://researchseminars.org/talk/CRMDS/13/
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