Covers of D-Type Artin Groups
Author(s) -
Meirav Amram,
Robert Shwartz,
Mina Teicher
Publication year - 2017
Publication title -
the electronic journal of combinatorics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.703
H-Index - 52
eISSN - 1097-1440
pISSN - 1077-8926
DOI - 10.37236/6146
Subject(s) - mathematics , semidirect product , combinatorics , artin group , quotient , graph , type (biology) , group (periodic table) , discrete mathematics , coxeter group , ecology , chemistry , organic chemistry , biology
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 $T$.
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