S. P. Glasby

activity

20102021

most citedDecomposing modular tensor products, and periodicity of `Jordan partitions'

4 citations · 10 across the 11 of their papers we have counts for

collaborators

11 papers

cs.IT2021★ 1 cited

Sequences of linear codes where the rate times distance grows rapidly

Faezeh Alizadeh, S. P. Glasby, Cheryl E. Praeger

For a linear code $C$ of length $n$ with dimension $k$ and minimum distance $d$ , it is desirable that the quantity $k d / n$ is large. Given an arbitrary field $F$ , we introd…

math.GR2021

The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger

Let $n, n^{'}$ be positive integers and let $V$ be an $(n + n^{'})$ -dimensional vector space over a finite field $F$ equipped with a non-degenerate alternating, hermitian or quadra…

math.GR2019★ 4 cited

Most permutations power to a cycle of small prime length

S. P. Glasby, Cheryl E. Praeger, W. R. Unger

We prove that most permutations of degree $n$ have some power which is a cycle of prime length approximately $lo g n$ . Explicitly, we show that for $n$ sufficiently large, the prop…

math.RT2017

`Norman involutions' and tensor products of unipotent Jordan blocks

S. P. Glasby, Cheryl E. Praeger, Binzhou Xia

A good knowledge of the Jordan canonical form (JCF) for a tensor product of `Jordan blocks' is key to understanding the actions of $p$ -groups of matrices in characteristic $p$ . The…

math.GR2016

Arc-transitive digraphs with quasiprimitive local actions

Michael Giudici, S. P. Glasby, Cai Heng Li +1

Let $Γ$ be a finite $G$ -vertex-transitive digraph. The in-local action of $(Γ, G)$ is the permutation group $L_{-}$ induced by the vertex-stabiliser on the set of in-neighbours of $v$ …

math.RT2014

Extraspecial towers and Weil representations

S. P. Glasby, R. B. Howlett

This paper was motivated by a remarkable group, the maximal subgroup $M = S_{3} ⋉ 2_{-}^{2 + 1} ⋉ 3^{2 + 1} ⋉ 2_{-}^{6 + 1}$ of the sporadic simple group $Fi_{23}$ , where…

math.RA2014

The density of uncyclic matrices

S. P. Glasby, Cheryl E. Praeger

An element $X$ in the algebra $M (n, F)$ of all $n \times n$ matrices over a field $F$ is said to be $f$ -cyclic if the underlying vector space considered as an…

math.GR2014

AS-configurations and skew-translation generalised quadrangles

John Bamberg, S. P. Glasby, Eric Swartz

The only known skew-translation generalised quadrangles (STGQ) having order $(q, q)$ , with $q$ even, are translation generalised quadrangles. Equivalently, the only known groups $G$ …

math.RT2014★ 1 cited

Decomposing modular tensor products: `Jordan partitions', their parts and p-parts

S. P. Glasby, Cheryl E. Praeger, Binzhou Xia

Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting module…

math.AC2014★ 4 cited

Decomposing modular tensor products, and periodicity of `Jordan partitions'

S. P. Glasby, Cheryl E. Praeger, Binzhou Xia

Let $J_{r}$ denote an $r \times r$ matrix over a finite field $F$ with minimal and characteristic polynomials $(t - 1)^{r}$ . Suppose $r \leq s$ . It is not hard to show that the Jordan cano…

math.GR2010

p-groups having a unique proper non-trivial characteristic subgroup

S. P. Glasby, P. P. Palfy, Csaba Schneider

We consider the structure of finite $p$ -groups $G$ having precisely three characteristic subgroups, namely $1$ , $Φ (G)$ and $G$ . The structure of $G$ varies markedly depending on wh…