We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group $A(T)$ is defined by a signed graph $T$. Then we find a certain quotient $G(T)$ according to the graph $T$, which also have a natural map onto $A(D_n)$. We prove that $G(T)$ is isomorphic to a semidirect product of a group $K^{(m,n)}$, with the Artin group $A(D_n)$, where $K^{(m,n)}$ depends only on the number $m$ of cycles and on the number $n$ of vertices of the graph $T$.
@article{10_37236_6146,
author = {Meirav Amram and Robert Shwartz and Mina Teicher},
title = {Covers of {D-type} {Artin} groups},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/6146},
zbl = {1439.20037},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6146/}
}
TY - JOUR
AU - Meirav Amram
AU - Robert Shwartz
AU - Mina Teicher
TI - Covers of D-type Artin groups
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6146/
DO - 10.37236/6146
ID - 10_37236_6146
ER -
%0 Journal Article
%A Meirav Amram
%A Robert Shwartz
%A Mina Teicher
%T Covers of D-type Artin groups
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6146/
%R 10.37236/6146
%F 10_37236_6146
Meirav Amram; Robert Shwartz; Mina Teicher. Covers of D-type Artin groups. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6146
