Alice C. Niemeyer

activity

20062026

most citedApportionment methods

24 citations · 86 across the 23 of their papers we have counts for

collaborators

28 papers

math.GR2026

The probability that two elements with large $1$ -eigenspaces generate a classical group

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

With high probability, among $O (lo g n)$ independent randomly selected elements from a finite $n$ -dimensional classical group, some pair of elements power to a $2$ -element generati…

math.RT2024

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger +1

This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $G L_{d} (F_{q})$ for which some element $g \in G$ of prime order $…

math.GR2024

Constructive Recognition of Special Linear Groups

Max Horn, Alice Niemeyer, Cheryl Praeger +1

We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d \times d$ matrices…

math.GR2023

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

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

Let $V := (F_{q})^{d}$ be a $d$ -dimensional vector space over the field $F_{q}$ of order $q$ . Fix positive integers $e_{1}, e_{2}$ satisfying $e_{1} + e_{2} = d$ . Motivated by analysi…

math.GR2021

Random generation of direct sums of finite non-degenerate subspaces

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

Let $V$ be a $d$ -dimensional vector space over a finite field $F$ equipped with a non-degenerate hermitian, alternating, or quadratic form. Suppose $∣ F ∣ = q^{2}$ if $…

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.GR2021

Conjugacy classes and centralisers in wreath products

Dominik Bernhardt, Alice C. Niemeyer, Friedrich Rober +1

In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a decomposition of elements of the full monomial group and exploit this to describe conj…

math.CO2019

A family of hemisystems on the parabolic quadrics

Jesse Lansdown, Alice C. Niemeyer

We constuct a family of hemisystems of the parabolic quadric $Q (2 d, q)$ , for all ranks $d \geq 2$ and all odd prime powers $q$ , that admit $Ω_{3} (q) ≅ PSL_{2} (q)$ …

math.GR2019

The icosahedra of edge length 1

Karl-Heinz Brakhage, Alice C. Niemeyer, Wilhelm Plesken +2

Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices toge…

math.GR2019★ 2 cited

Irreducible linear subgroups generated by pairs of matrices with large irreducible submodules

Alice C. Niemeyer, Sabina B. Pannek, Cheryl E. Praeger

We call an element of a finite general linear group $GL (d, q)$ \emph{fat} if it leaves invariant, and acts irreducibly on, a subspace of dimension greater than $d /2$ . Fat…

math.RA2018★ 1 cited

A parallel algorithm for Gaussian elimination over finite fields

Stephen Linton, Gabriele Nebe, Alice Niemeyer +2

In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large i…

math.GR2018★ 13 cited

A Finite Soluble Quotient Algorithm

Alice C. Niemeyer

An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an…

math.GR2017

On the second-largest Sylow subgroup of a finite simple group of Lie type

S. P. Glasby, Alice C. Niemeyer, Tomasz Popiel

Let $T$ be a finite simple group of Lie type in characteristic $p$ , and let $S$ be a Sylow subgroup of $T$ with maximal order. It is well known that $S$ is a Sylow $p$ -subgroup exc…

math.GR2017★ 3 cited

On permutations of order dividing a given integer

Alice C. Niemeyer, Cheryl E. Praeger

We give a detailed analysis of the proportion of elements in the symmetric group on $n$ points whose order divides $m$ , for $n$ sufficiently large and $m \geq n$ with $m = O (n)$ .

math.GR2016

The Divisibility Graph of finite groups of Lie Type

Adeleh Abdolghafourian, Mohammad A. Iranmanesh, Alice C. Niemeyer

The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divid…

math.GR2016

Maximal linear groups induced on the Frattini quotient of a $p$ -group

John Bamberg, S. P. Glasby, Luke Morgan +1

Let $p > 3$ be a prime. For each maximal subgroup $H ⩽ GL (d, p)$ with $∣ H ∣ ⩾ p^{3 d + 1}$ , we construct a $d$ -generator finite $p$ -group $G$ with the property that…

math.GR2015★ 1 cited

On the Complexity of Multiplication in the Iwahori--Hecke Algebra of the Symmetric Group

Alice C. Niemeyer, Götz Pfeiffer, Cheryl E. Praeger

We present new efficient data structures for elements of Coxeter groups of type $A_{m}$ and their associated Iwahori--Hecke algebras $H (A_{m})$ . Usually, elements of $H (A_{m})$ are repre…

math.HO2015★ 24 cited

Apportionment methods

Horst F. Niemeyer, Alice C. Niemeyer

Most democratic countries use election methods to transform election results into whole numbers which usually give the number of seats in a legislative body the parties obtained. W…

math.GR2015

Finding involutions with small support

Alice C. Niemeyer, Tomasz Popiel

We show that the proportion of permutations $g$ in $S_{n}$ or $A_{n}$ such that $g$ has even order and $g^{∣ g ∣/2}$ is an involution with support of cardinality at most $\lceil n^\varep…

math.NT2015★ 8 cited

Primitive prime divisors and the $n$ -th cyclotomic polynomial

S. P. Glasby, Frank Lübeck, Alice C. Niemeyer +1

Primitive prime divisors play an important role in group theory and number theory. We study a certain number theoretic quantity, called $Φ_{n}^{*} (q)$ , which is closely related to the…

math.GR2014

Elements in finite classical groups whose powers have large 1-Eigenspaces

Alice C. Niemeyer, Cheryl E. Praeger

We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point…

math.GR2014

On complexity of multiplication in finite soluble groups

M. F. Newman, Alice C. Niemeyer

We determine a reasonable upper bound for the complexity of collection from the left to multiply two elements of a finite soluble, or polycyclic, group by restricting attention to…

math.GR2013★ 9 cited

Fast recognition of alternating groups of unknown degree

Sebastian Jambor, Martin Leuner, Alice C. Niemeyer +1

We present a constructive recognition algorithm to decide whether a given black-box group is isomorphic to an alternating or a symmetric group without prior knowledge of the degree…

cs.DS2013

Showcasing straight-line programs with memory via matrix Bruhat decomposition

Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger +1

We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of f…

The probability that two elements with large 1-eigenspaces generate a classical group

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

Constructive Recognition of Special Linear Groups

Bipartite q-Kneser graphs and two-generated irreducible linear groups

Random generation of direct sums of finite non-degenerate subspaces

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

Conjugacy classes and centralisers in wreath products

A family of hemisystems on the parabolic quadrics

The icosahedra of edge length 1

Irreducible linear subgroups generated by pairs of matrices with large irreducible submodules

A parallel algorithm for Gaussian elimination over finite fields

A Finite Soluble Quotient Algorithm

On the second-largest Sylow subgroup of a finite simple group of Lie type

On permutations of order dividing a given integer

The Divisibility Graph of finite groups of Lie Type

Maximal linear groups induced on the Frattini quotient of a p-group

On the Complexity of Multiplication in the Iwahori--Hecke Algebra of the Symmetric Group

Apportionment methods

Finding involutions with small support

Primitive prime divisors and the n-th cyclotomic polynomial

Elements in finite classical groups whose powers have large 1-Eigenspaces

On complexity of multiplication in finite soluble groups

Fast recognition of alternating groups of unknown degree

Showcasing straight-line programs with memory via matrix Bruhat decomposition

The probability that two elements with large $1$ -eigenspaces generate a classical group

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

Maximal linear groups induced on the Frattini quotient of a $p$ -group

Primitive prime divisors and the $n$ -th cyclotomic polynomial