A presentation for the unipotent group over rings with identity

Published

Journal Article

For a ring R with identity, define Unipn(R) to be the group of upper-triangular matrices over R all of whose diagonal entries are 1. For i = 1,2,...,n - 1, let Si denote the matrix whose only nonzero off-diagonal entry is a 1 in the ith row and (i + 1)st column. Then for any integer m (including m = 0), it is easy to see that the Si generate Unipn(Z/mZ). Reiner gave relations among the Si which he conjectured gave a presentation for Unipn(Z/2Z). This conjecture was proven by Biss [Comm. Algebra26 (1998), 2971-2975] and an analogous conjecture was made for Unipn(Z/mZ) in general. We prove this conjecture, as well as a generalization of the conjecture to unipotent groups over arbitrary rings. © 2001 Academic Press.

Full Text

Duke Authors

Cited Authors

  • Biss, DK; Dasgupta, S

Published Date

  • March 15, 2001

Published In

Volume / Issue

  • 237 / 2

Start / End Page

  • 691 - 707

International Standard Serial Number (ISSN)

  • 0021-8693

Digital Object Identifier (DOI)

  • 10.1006/jabr.2000.8604

Citation Source

  • Scopus