Limit groups over coherent right-angled Artin groups
Casals-Ruiz, Montserrat (IKERBASQUE. Zientziarako Euskal Fundazioa)
Kazachkov, Ilya (IKERBASQUE. Zientziarako Euskal Fundazioa)
Duncan, Andrew (Newcastle University. School of Mathematics, Statistics and Physics)

Date:	2023
Abstract:	A new class of groups C, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group G in the class C, the Z[t]-exponential group GZ[t] may be constructed as an iterated centraliser extension. Using this fact, it is proved that GZ[t] is fully residually G (i. e. it has the same universal theory as G) and so its finitely generated subgroups are limit groups over G. If G is a coherent RAAG, then the converse also holds - any limit group over G embeds into GZ[t]. Moreover, it is proved that limit groups over G are finitely presented, coherent and CAT(0), so in particular have solvable word and conjugacy problems.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; Versió publicada
Subject:	Partially commutative group ; Right-angled artin group ; Limit group ; Hyperbolic group
Published in:	Publicacions matemàtiques, Vol. 67 Núm. 1 (2023) , p. 199-199-257 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/412634
DOI: 10.5565/PUBLMAT6712305

59 p, 606.6 KB

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