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(Dn). We prove that G(T) is isomorphic to a semidirect product of a group K(m,n), with the Artin group A(Dn), where K(m,n) depends only on the number m of cycles and on the number n of vertices of the graph T.
Bibliographical noteFunding Information:
∗Partially supported by the Emmy Noether Research Institute for Mathematics (center of the Minerva Foundation of Germany), the Excellency Center ”Group Theoretic Methods in the Study of Algebraic Varieties” of the Israel Science Foundation, and EAGER (EU network, HPRN-CT-2009-00099)
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- Artin groups
- Signed graphs