Math @ Duke

Publications [#338523] of Samit Dasgupta
Papers Published
 Biss, DK; Dasgupta, S, A presentation for the unipotent group over rings with identity,
Journal of Algebra, vol. 237 no. 2
(March, 2001),
pp. 691707, Elsevier BV [doi]
(last updated on 2022/01/25)
Abstract: For a ring R with identity, define Unipn(R) to be the group of uppertriangular matrices over R all of whose diagonal entries are 1. For i = 1,2,...,n  1, let Si denote the matrix whose only nonzero offdiagonal 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), 29712975] 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.


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