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Universal groups for right-angled buildings

Tom De Medts (UGent) , Ana Filipa Costa da Silva (UGent) and Koen Struyve (UGent)
(2018) GROUPS GEOMETRY AND DYNAMICS. 12(1). p.231-287
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Abstract
2000, M. Burger and S. Mozes introduced universal groups acting on trees with a prescribed local action. We generalize this concept to groups acting on right-angled buildings. When the right-angled building is thick and irreducible of rank at least 2 and each of the local permutation groups is transitive and generated by its point stabilizers, we show that the corresponding universal group is a simple group. When the building is locally finite, these universal groups are compactly generated totally disconnected locally compact groups, and we describe the structure of the maximal compact open subgroups of the universal groups as a limit of generalized wreath products.
Keywords
Right-angled buildings, totally disconnected locally compact groups, universal groups, simple groups

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Citation

Please use this url to cite or link to this publication:

MLA
De Medts, Tom, Ana Filipa Costa da Silva, and Koen Struyve. “Universal Groups for Right-angled Buildings.” GROUPS GEOMETRY AND DYNAMICS 12.1 (2018): 231–287. Print.
APA
De Medts, T., Costa da Silva, A. F., & Struyve, K. (2018). Universal groups for right-angled buildings. GROUPS GEOMETRY AND DYNAMICS, 12(1), 231–287.
Chicago author-date
De Medts, Tom, Ana Filipa Costa da Silva, and Koen Struyve. 2018. “Universal Groups for Right-angled Buildings.” Groups Geometry and Dynamics 12 (1): 231–287.
Chicago author-date (all authors)
De Medts, Tom, Ana Filipa Costa da Silva, and Koen Struyve. 2018. “Universal Groups for Right-angled Buildings.” Groups Geometry and Dynamics 12 (1): 231–287.
Vancouver
1.
De Medts T, Costa da Silva AF, Struyve K. Universal groups for right-angled buildings. GROUPS GEOMETRY AND DYNAMICS. 2018;12(1):231–87.
IEEE
[1]
T. De Medts, A. F. Costa da Silva, and K. Struyve, “Universal groups for right-angled buildings,” GROUPS GEOMETRY AND DYNAMICS, vol. 12, no. 1, pp. 231–287, 2018.
@article{8564003,
  abstract     = {{2000, M. Burger and S. Mozes introduced universal groups acting on trees with a prescribed local action. We generalize this concept to groups acting on right-angled buildings. When the right-angled building is thick and irreducible of rank at least 2 and each of the local permutation groups is transitive and generated by its point stabilizers, we show that the corresponding universal group is a simple group. 
When the building is locally finite, these universal groups are compactly generated totally disconnected locally compact groups, and we describe the structure of the maximal compact open subgroups of the universal groups as a limit of generalized wreath products.}},
  author       = {{De Medts, Tom and Costa da Silva, Ana Filipa and Struyve, Koen}},
  issn         = {{1661-7207}},
  journal      = {{GROUPS GEOMETRY AND DYNAMICS}},
  keywords     = {{Right-angled buildings,totally disconnected locally compact groups,universal groups,simple groups}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{231--287}},
  title        = {{Universal groups for right-angled buildings}},
  url          = {{http://dx.doi.org/10.4171/ggd/443}},
  volume       = {{12}},
  year         = {{2018}},
}

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