Diameters of Chevalley groups over local rings
نویسندگان
چکیده
منابع مشابه
Diameters of Cayley graphs of Chevalley groups
We show that for integers k ≥ 2 and n ≥ 3, the diameter of the Cayley graph of SLn(Z/kZ) associated to a standard two-element generating set, is at most a constant times n ln k. This answers a question of A. Lubotzky concerning SLn(Fp) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing element...
متن کاملChevalley Groups over Commutative Rings I. Elementary Calculations
This is the rst in a series of papers dedicated to the structure of Chevalley groups over commutative rings. The goal of this series is to systematically develop methods of calculations in Chevalley groups over rings, based on the use of their minimal modules. As an application we give new direct proofs for normality of the elementary subgroup, description of normal subgroups and similar result...
متن کاملOrthogonal Groups over Local Rings
In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...
متن کاملChow Rings and Cobordism of Some Chevalley Groups
We compute the cobordism rings of the classifying spaces of a certain class of Chevalley groups. In the particular case of the general linear group, we prove that it is isomorphic to the Chow ring.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2012
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-012-0451-6