Outer automorphisms of upper triangular matrices
type: Item
instance of: scholarly article
title: Outer automorphisms of upper triangular matrices
zbMATH Open document ID: 0815.20037
published in: Journal of Algebra
publication date: 1995-07-04T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/30473
review text: Let \(U_ n\) be the subgroup of upper triangular matrices in \(\text{GL}_ n(\mathbb{F}_ 2)\). The author calculates the outer automorphism group of \(U_ n\), which is generated by the ``flip'' (or anti-transpose), the central automorphisms and the extremal automorphisms. This implies that the classifying space \(BU_ 4\) has three dominant summands, and \(BU_ n\) has only one dominant summand for \(n \geq 5\).
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H30
zbMATH DE Number: 554241
zbMATH Keywords: subgroup of upper triangular matrices
zbMATH Keywords: outer automorphism group
zbMATH Keywords: anti- transpose
zbMATH Keywords: central automorphisms
zbMATH Keywords: extremal automorphisms
zbMATH Keywords: classifying space
zbMATH Keywords: dominant summands
author: John S. Maginnis
MaRDI profile type: Publication
OpenAlex ID: W1977012029
DOI: 10.1006/JABR.1993.1218
description: scientific article; zbMATH DE number 554241