Fixed fields of triangular matrix groups

Involutions and characters of upper triangular matrix groups

We study the realizability over R of representations of the group U(n) of upper-triangular n× n matrices over F2. We prove that all the representations of U(n) are realizable over R if n ≤ 12, but that if n ≥ 13, U(n) has representations not realizable over R. This theorem is a variation on a result that can be obtained by combining work of J. Arregi and A. Vera-López and of the authors, but th...

Differential Polynomial Rings of Triangular Matrix Rings

Recognizing finite matrix groups over infinite fields

Article history: Received 12 January 2012 Accepted 10 April 2012 Available online 15 June 2012

Computing with Matrix Groups over Infinite Fields

We survey currently available algorithms for computing with matrix groups over infinite domains. We discuss open problems in the area, and avenues for further development.

Fixed point free automorphisms of groups related to finite fields

Let G = Fqo 〈β〉 be the semidirect product of the additive group of the field of q = p elements and the cyclic group of order d generated by the invertible linear transformation β defined by multiplication by a power of a primitive root of Fq. We study endomorphisms of G. We find an arithmetic condition on d so that every endomorphism is determined by its values on (1, 1) and (0, β). When that i...