Transitivity properties for group actions on buildings

Peter Abramenko, Kenneth S. Brown

Type: Article

Publication Date: 2007-01-23

Citations: 10

DOI: https://doi.org/10.1515/jgt.2007.021

Abstract

We study two transitivity properties for group actions on buildings, called Weyl transitivity and strong transitivity. Following hints by Tits, we give examples involving anisotropic algebraic groups to show that strong transitivity is strictly stronger than Weyl transitivity. A surprising feature of the examples is that strong transitivity holds more often than expected.

Locations

Journal of Group Theory - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	Buildings of Spherical Type and Finite BN-Pairs	1974	Jacques Tits
+	Lectures on buildings	1990	Mark Ronan
+	A Course in Arithmetic	1973	Jean Pierre Serre
+	Algebraic groups and number theory	1992	В. П. Платонов Andrei S. Rapinchuk
+	Éléments de mathématique	2006	Nicolás Bourbaki
+	Introduction to Quadratic Forms	1973	O. T. O’Meara
+	Introduction to Quadratic Forms over Fields	2004	T. Y. Lam
+	Quadratic and Hermitian Forms	1985	Winfried Scharlau
+	Groupes Réductifs Sur Un Corps Local	1972	François Bruhat Jacques Tits