4 citations · 19 across the 29 of their papers we have counts for
6 papers · 1 filter
Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators
S. P. Glasby
The group U_n(F) of all nxn unipotent upper-triangular matrices over F has derived length d := Ceiling(log_2 (n)), equivalently 2^{d-1} < n <= 2^d. We prove that U_n(F) has a 3-gen…
Point-primitive generalised hexagons and octagons
John Bamberg, S. P. Glasby, Tomasz Popiel +2
In 2008, Schneider and Van Maldeghem proved that if a group acts flag-transitively, point-primitively, and line-primitively on a generalised hexagon or generalised octagon, then it…
Generalised quadrangles and transitive pseudo-hyperovals
John Bamberg, Stephen P. Glasby, Tomasz Popiel +1
A pseudo-hyperoval of a projective space $\PG(3n-1,q)$, even, is a set of subspaces of dimension such that any three span the whole space. We prove that a pseudo-…
Writing representations over minimal fields
S. P. Glasby, R. B. Howlett
The chief aim of this paper is to describe a procedure which, given a -dimensional absolutely irreducible matrix representation of a finite group over a finite field $\mathbb{E}…
Distant parents in complete binary trees
S. P. Glasby
There is a unique path from the root of a tree to any other vertex. Every vertex, except the root, has a parent: the adjoining vertex on this unique path. This is the conventional…
Using recurrence relations to count in symmetric groups
S. P. Glasby
We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group in order to construct recurrence relations for enumerating certain…