Solution of the Problem of Equality and Conjugacy of Words in a Certain Class of Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

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Separating quasiconvex subgroups of right-angled Artin groups

Mathematische Zeitschrift ◽

10.1007/s002090100329 ◽

2002 ◽

Vol 240 (3) ◽

pp. 521-548 ◽

Cited By ~ 7

Author(s):

Tim Hsu ◽

Daniel T. Wise

Keyword(s):

Artin Groups ◽

Right Angled Artin Groups ◽

Quasiconvex Subgroups

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The BNS-invariant for some Artin groups of arbitrary circuit rank

Journal of Group Theory ◽

10.1515/jgth-2016-0057 ◽

2017 ◽

Vol 20 (4) ◽

Cited By ~ 2

Author(s):

Kisnney Almeida

Keyword(s):

Artin Groups

AbstractWe classify the Bieri–Neumann–Strebel invariant

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On a conjecture in Artin groups

International Journal of Algebra and Computation ◽

10.1142/s0218196721400105 ◽

2021 ◽

pp. 1-25

Author(s):

Arye Juhász

Keyword(s):

Artin Group ◽

Two Dimensional ◽

Artin Groups ◽

Small Cancellation ◽

Small Cancellation Theory ◽

Infinite Type ◽

Trivial Center

It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

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