764 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University College DublinIE182 papers
- Center for Astrophysics Harvard & SmithsonianUS167 papers
- Purdue University West LafayetteUS154 papers
- McGill UniversityCA153 papers
- University of California, Santa CruzUS151 papers
- Washington University in St. LouisUS150 papers
- Iowa State UniversityUS149 papers
- University of California, Los AngelesUS149 papers
- University of UtahUS149 papers
- Columbia UniversityUS138 papers
- Munster Technological UniversityIE138 papers
- University of ChicagoUS138 papers
26 papers · 1 filter
Smooth cuboids in group theory
Joshua Maglione, Mima Stanojkovski
A smooth cuboid can be identified with a matrix of linear forms, with coefficients in a field , whose determinant describes a smooth cubic in the projective plane. T…
Algorithms for computing with nilpotent matrix groups over infinite domains
A. S. Detinko, D. L. Flannery
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particula…
Algorithms for arithmetic groups with the congruence subgroup property
A. S. Detinko, D. L. Flannery, A. Hulpke
We develop practical techniques to compute with arithmetic groups for . Our approach relies on constructing a principal congruence subgroup i…
Deciding finiteness of matrix groups in positive characteristic
A. S. Detinko, D. L. Flannery, E. A. O'Brien
We present a new algorithm to decide finiteness of matrix groups defined over a field of positive characteristic. Together with previous work for groups in zero characteristic, thi…
Recognizing finite matrix groups over infinite fields
A. S. Detinko, D. L. Flannery, E. A. O'Brien
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finite…
The strong approximation theorem and computing with linear groups
Alla Detinko, Dane Flannery, Alexander Hulpke
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely g…
Experimenting with symplectic hypergeometric monodromy groups
A. S. Detinko, D. L. Flannery, A. Hulpke
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, somet…
L.G. Kovács and linear groups
A. S. Detinko, D. L. Flannery
We survey the legacy of L.G. Kovács in linear group theory, with a particular focus on classification questions.
Practical computation with linear groups over infinite domains
A. Detinko, D. Flannery
We survey recent progress in computing with finitely generated linear groups over infinite fields, describing the mathematical background of a methodology applied to design practic…
Linear groups and computation
A. S. Detinko, D. L. Flannery
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodolo…
Algorithms for experimenting with Zariski dense subgroups
Alla Detinko, Dane Flannery, Alexander Hulpke
We give a method to describe all congruence images of a finitely generated Zariski dense group . The method is applied to obtain efficient algori…
On the Table of Marks of a Direct Product of Finite Groups
Brendan Masterson, Götz Pfeiffer
We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of…
Zariski Density and Computing in Arithmetic Groups
Alla Detinko, Dane Flannery, Alexander Hulpke
For , let denote either or . We give a practical algorithm to compute the level of the maximal principal congruence subgroup in an arithmetic group…
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…
Geometric dimension of lattices in classical simple Lie groups
Javier Aramayona, Dieter Degrijse, Conchita Martinez-Perez +1
We prove that if is a lattice in a classical simple Lie group , then the symmetric space of is -equivariantly homotopy equivalent to a proper cocompact -CW complex…
Commensurations and Metric Properties of Houghton's Groups
José Burillo, Sean Cleary, Armando Martino +1
We describe the automorphism groups and the abstract commensurators of Houghton's groups. Then we give sharp estimates for the word metric of these groups and deduce that the comme…
Obstructions for subgroups of Thompson's group
José Burillo, Sean Cleary, Claas E. Röver
Thompson's group has a rich variety of subgroups, containing all finite groups, all finitely generated free groups and all finitely generated abelian groups, the finitary permu…
Unitary groups over local rings
J. Cruickshank, A. Herman, R. Quinlan +1
Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finit…
Addendum to "Commensurations and Subgroups of Finite Index of Thompson's Group F"
José Burillo, Sean Cleary, Claas E. Röver
We show that the abstract commensurator of Thompson's group F is composed of four building blocks: two isomorphism types of simple groups, the multiplicative group of the positive…
On the Quiver Presentation of the Descent Algebra of the Symmetric Group
Marcus Bishop, Götz Pfeiffer
We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent alge…
Group ring cryptography
Barry Hurley, Ted Hurley
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking pow…
The Mod-2 Cohomology Ring of the Third Conway Group is Cohen-Macaulay
Simon A. King, David J. Green, Graham Ellis
By explicit machine computation we obtain the mod-2 cohomology ring of the third Conway group Co_3. It is Cohen-Macaulay, has dimension 4, and is detected on the maximal elementary…
A Note on Element Centralizers in Finite Coxeter Groups
Matjaž Konvalinka, Götz Pfeiffer, Claas Röver
The normalizer of a standard parabolic subgroup of a finite Coxeter group splits over the parabolic subgroup with complement consisting of certain minima…
The computation of the cohomology rings of all groups of order 128
David J. Green, Simon A. King
We describe the computation of the mod-2 cohomology rings of all 2328 groups of order 128. One consequence is that all groups of order less than 256 satisfy the strong form of Bens…