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The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right‐angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible spherical special subgroups of the Artin group, and conjecture that sufficiently large powers of those elements generate an obvious right‐angled Artin subgroup. This alleged right‐angled Artin subgroup is in some sense as large as possible; its nerve is homeomorphic to the nerve of the ambient Artin group. We verify this conjecture for the class of locally reducible Artin groups, which includes all 2$\hskip.001pt 2$‐dimensional Artin groups, and for spherical Artin groups of any type other than E6,E7,E8$E_6, E_7, E_8$. We use our results to conclude that certain Artin groups contain hyperbolic surface subgroups, answering questions of Gordon, Long and Reid. [ABSTRACT FROM AUTHOR]

In a recent article, Cumplido and Paris studied the question of commensurability between Artin groups of spherical type. Their analysis left six cases undecided, for the following pairs of Artin groups: (F 4 , D 4) , (H 4 , D 4) , (F 4 , H 4) , (E 6 , D 6) , (E 7 , D 7) , and (E 8 , D 8). In this note we resolve the first two of these cases, namely, we show that the Artin groups of types F 4 and H 4 are not commensurable with that of type D 4. As a key step, we realize the abstract commensurator of the Artin group of type D 4 as the extended mapping class group of the torus with three punctures. We also find the automorphism group of the Artin group of type D 4 and obtain a description of torsion elements, their orders and conjugacy classes in all irreducible Artin groups of spherical type modulo their centers. • The automorphism group and the commensurator of Artin group of type D 4 are found. • Torsion elements in the central quotients of spherical Artin groups are classified. • It is proved that Artin groups of types H 4 and D 4 are not commensurable. • It is proved that Artin groups of types F 4 and D 4 are not commensurable. [ABSTRACT FROM AUTHOR]