On commensurability of right-angled Artin groups II: RAAGs defined by paths
Keyword(s):
Abstract In this paper we continue the study of right-angled Artin groups up to commensurability initiated in [CKZ]. We show that RAAGs defined by different paths of length greater than 3 are not commensurable. We also characterise which RAAGs defined by paths are commensurable to RAAGs defined by trees of diameter 4. More precisely, we show that a RAAG defined by a path of length n > 4 is commensurable to a RAAG defined by a tree of diameter 4 if and only if n ≡ 2 (mod 4). These results follow from the connection that we establish between the classification of RAAGs up to commensurability and linear integer-programming.
Keyword(s):
2014 ◽
Vol 14
(3)
◽
pp. 1677-1743
◽
2018 ◽
Vol 117
(5)
◽
pp. 901-950
◽