SURFACE SUBGROUPS OF GRAPH PRODUCTS OF GROUPS

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Let G be a graph product of a collection of groups and H be the direct product of the same collection of groups, so that there is a natural surjection p : G -> H. The kernel of this map p is called a graph product kernel. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups is virtually cocompact special in the sense of Haglund and Wise. The proof of this yields conditions for a graph over which the graph product of arbitrary nontrivial groups (or some cyclic groups, or some finite groups) contains a hyperbolic surface group. In particular, the graph product of arbitrary nontrivial groups over a cycle of length at least five, or over its opposite graph, contains a hyperbolic surface group. For the case when the defining graphs have at most seven vertices, we completely characterize right-angled Coxeter groups with hyperbolic surface subgroups.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2012-12
Language
English
Article Type
Article; Proceedings Paper
Keywords

ANGLED ARTIN GROUPS; COXETER GROUPS

Citation

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v.22, no.8

ISSN
0218-1967
DOI
10.1142/S0218196712400036
URI
http://hdl.handle.net/10203/102254
Appears in Collection
MA-Journal Papers(저널논문)
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