A family of \(\widetilde A_n\)-groups
type: Item
instance of: scholarly article
title: A family of \(\widetilde A_n\)-groups
zbMATH Open document ID: 0923.51010
DOI: 10.1007/BF02762271
author: Donald I. Cartwright
author: Tim Steger
published in: Israel Journal of Mathematics
publication date: 1999-10-06T00:00:00Z
review text: The authors establish for each finite field \(k\), for each natural number \(n\geq 2\), and for each automorphism \(\sigma\) of \(k\), an automorphism group of the affine building \(\Delta\) of type \(\widetilde A_n\) associated to \(k(t)\) acting sharply transitively and type-rotating on the set of vertices of \(\Delta\). This uses the lattice construction of the affine building \(\Delta\) and generalizes earlier results for \(n=2,3\).
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 1250643
zbMATH Keywords: vertex-regular group
zbMATH Keywords: affine building
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
cites work: Groups acting simply transitively on the vertices of a building of type \(\tilde A_ 2\). I
cites work: Groups acting simply transitively on the vertices of a building of type \(\tilde A_ 2\). II: The cases \(q=2\) and \(q=3\)
cites work: Q3997571
cites work: PI-algebras. An introduction
cites work: Q3286355
cites work: Q4692803
full work available at URL: https://doi.org/10.1007/bf02762271
OpenAlex ID: W2325965674
description: scientific article; zbMATH DE number 1250643