scholarly journals Relative automorphism groups of right‐angled Artin groups

2019 ◽  
Vol 12 (3) ◽  
pp. 759-798 ◽  
Author(s):  
Matthew B. Day ◽  
Richard D. Wade
Keyword(s):  
Automorphism Groups ◽  
Artin Groups ◽  
Right Angled Artin Groups

scholarly journals Trees, homology, and automorphism groups of right-angled Artin groups

2018 ◽  
Vol 50 (3) ◽  
pp. 293-315
Author(s):  
Javier Aramayona ◽  
José L. Fernández ◽  
Pablo Fernández ◽  
Conchita Martínez-Pérez
Keyword(s):  
Automorphism Groups ◽  
Artin Groups ◽  
Right Angled Artin Groups

scholarly journals ON SOLVABLE SUBGROUPS OF AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS

2011 ◽  
Vol 21 (01n02) ◽  
pp. 61-70 ◽  
Author(s):  
MATTHEW B. DAY
Keyword(s):  
Automorphism Group ◽  
Finite Index ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Free Subgroup ◽  
Artin Group ◽  
Artin Groups ◽  
Alternative Theorem ◽  
Right Angled Artin Groups ◽  
Defining Graph

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a non-obvious way.

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled 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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