Covers of D-Type Artin Groups

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 prov...

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Veröffentlicht in:The Electronic journal of combinatorics 2017-10, Vol.24 (4)
Hauptverfasser: Amram, Meirav, Shwartz, Robert, Teicher, Mina
Format: Artikel
Sprache:eng
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Zusammenfassung: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 $T$.
ISSN:1077-8926
1077-8926
DOI:10.37236/6146