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Groups, periodic planes and hyperbolic buildings
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Alina Vdovina
Published/Copyright:
November 18, 2005
Abstract
Using methods of combinatorial group theory, we give an elementary construction of polyhedra whose links are (not necessarily isomorphic) connected bipartite graphs. In particular, we construct polyhedra whose links are generalized m -gons. Polyhedra of this type are interesting because their universal coverings are two-dimensional hyperbolic buildings with different links. We show that the fundamental groups of some of our polyhedra contain surface groups. The presentation of the results is given in the language of combinatorial group theory.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
