Matrix generators for J3

Standard Generators for J3

Matrix generators for the Ree groups

For the purposes of [K] and [KM] it became necessary to have 7× 7 matrix generators for a Sylow-3-subgroup of the Ree groups G2(q) and its normalizer. For example in [K] we wanted to show that in a seven dimensional representation the Jordan canonical form of any element of order nine is a single Jordan block of size 7. In [KM] we develop group recognition algorithms. At some stage we need to i...

Matrix Generators for the Orthogonal Groups

1. Introduction Generators for the groups SL(l; q), Sp(2m; q), U(l; q) and Sz(q) have been available in computer algebra systems for some time 1, 4, 12]. Until recently it has only been practical to work with these groups for small dimensions and small elds. This covered small orthogonal groups (but not in their natural representation) because the orthogonal groups up to dimension 6 are isomorp...

Matrix generators for the Harada-Norton group

Generators of matrix incidence algebras

Let n E Z+ and let K be a field. Let ~ be a partial order on {1, 2, ... , n}. Let An(:::;) be the matrix incidence algebra consisting of those n x n matrices A = (ai,j) with entries in K, satisfying ai,j 0 whenever i 1:. j. For a subset £ ~ An (::5), a necessary and sufficient condition that the algebra generated by £ u {I} is An(::5) is that (i) for every 1 :::; i, j :::; n with i =1= j, there...