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SUMMARY:Generating RAAGs in 1-relator groups - Ashot Minasyan\, Southampto
 n
DTSTART:20240216T134500Z
DTEND:20240216T144500Z
UID:TALK205783@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:Given a finite simplicial graph $\\Gamma$\, the right angled A
 rtin group (RAAG) $A(\\Gamma)$ is generated by the vertices of $\\Gamma$ s
 ubject to the relations that two vertices commute if and only if they are 
 adjacent in $\\Gamma$. The monoid with the same presentation is called the
  trace monoid $T(\\Gamma)$. RAAGs play an important role in Geometric Grou
 p Theory\, while Trace monoids originated in Computer Science. \n\nThe tra
 ce monoid $T(\\Gamma)$ is naturally embedded in the RAAG $A(\\Gamma)$\, as
  the set of positive words. In my talk I will discuss the following proble
 m: suppose that a 1-relator group G contains a submonoid isomorphic to $T(
 \\Gamma)$. Does $G$ also contain a copy of $A(\\Gamma)$ as a subgroup?\n\n
 This problem is motivated by recent work of Foniqi\, Gray and Nyberg-Brodd
 a\, who proved that groups containing T(P_4)\, where P_4 is the path with 
 4 vertices (of length 3)\, have undecidable rational subset problem. They 
 also exhibited 1-relator groups containing A(P_4) and asked whether every 
 1-relator group which has a submonoid isomorphic to T(P_4) must also have 
 a subgroup isomorphic to A(P_4). I will sketch an argument\, based on join
 t work with Motiejus Valiunas (University of Wroclaw\, Poland)\, showing t
 hat the answer to the latter question is positive.\n
LOCATION:MR13
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