24 citations · 86 across the 23 of their papers we have counts for
21 papers · 1 filter
The probability that two elements with large -eigenspaces generate a classical group
S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger
With high probability, among independent randomly selected elements from a finite -dimensional classical group, some pair of elements power to a -element generati…
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 generated by a set of matrices…
Bipartite -Kneser graphs and two-generated irreducible linear groups
S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger
Let be a -dimensional vector space over the field of order . Fix positive integers satisfying . Motivated by analysi…
Random generation of direct sums of finite non-degenerate subspaces
S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger
Let be a -dimensional vector space over a finite field equipped with a non-degenerate hermitian, alternating, or quadratic form. Suppose if $…
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 be positive integers and let be an -dimensional vector space over a finite field equipped with a non-degenerate alternating, hermitian or quadra…
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…
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…
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 \emph{fat} if it leaves invariant, and acts irreducibly on, a subspace of dimension greater than . Fat…
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…
On the second-largest Sylow subgroup of a finite simple group of Lie type
S. P. Glasby, Alice C. Niemeyer, Tomasz Popiel
Let be a finite simple group of Lie type in characteristic , and let be a Sylow subgroup of with maximal order. It is well known that is a Sylow -subgroup exc…
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 points whose order divides , for sufficiently large and with .
The Divisibility Graph of finite groups of Lie Type
Adeleh Abdolghafourian, Mohammad A. Iranmanesh, Alice C. Niemeyer
The Divisibility Graph of a finite group has vertex set the set of conjugacy class lengths of non-central elements in and two vertices are connected by an edge if one divid…
Maximal linear groups induced on the Frattini quotient of a -group
John Bamberg, S. P. Glasby, Luke Morgan +1
Let be a prime. For each maximal subgroup with , we construct a -generator finite -group with the property that…
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 and their associated Iwahori--Hecke algebras . Usually, elements of are repre…
Finding involutions with small support
Alice C. Niemeyer, Tomasz Popiel
We show that the proportion of permutations in or such that has even order and is an involution with support of cardinality at most $\lceil n^\varep…
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…
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…
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…
Abundant p-singular elements in finite classical groups
Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger
In 1995, Isaacs, Kantor and Spaltenstein proved that for a finite simple classical group G defined over a field with q elements, and for a prime divisor p of |G| distinct from the…
Identifying long cycles in finite alternating and symmetric groups acting on subsets
Steve Linton, Alice C. Niemeyer, Cheryl E. Praeger
Let be a permutation group on a set , which is permutationally isomorphic to a finite alternating or symmetric group or acting on the -element subsets of poin…
On the frequency of permutations containing a long cycle
Alice C. Niemeyer, Cheryl E. Praeger
A general explicit upper bound is obtained for the proportion of elements of order dividing , where for some constant , in the finite symmetric gr…