Automorphism groups of some affine and finite type Artin groups
Ruth Charney, John Crisp
Abstract
We observe that, for each positive integer n > 2, each of the Artin groups of finite type An, Bn=Cn, and affine type An-1 and Cn-1 is a central extension of a finite index subgroup of the mapping class group of the (n+2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping class groups we are able to determine the automorphism groups of each member of these four infinite families of Artin groups.
Create a lesson
Related papers
Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
Ignat Soroko
DL, DQ Spectrum and Eigenvalue-free Interval of Cayley Graphs over Finite Nilpotent Groups
Pallabi Manna, Santanu Mandal
On p-groups with one nonlinear codegree
Jiwei Zheng, Heng Lv
Classes of Subgroups of a finite group with isomorphic quotient groups
Tushar Halder, Sachin Ballal
Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
On the number of conjugacy classes of finite solvable groups of order divisible by p2
Thomas Michael Keller