12 citations · 30 across the 20 of their papers we have counts for
18 papers · 1 filter
Nilpotent primitive linear groups over finite fields
A. S. Detinko, D. L. Flannery
We provide a detailed structural description of the nilpotent primitive subgroups of , where is a finite field.
Zariski density and computing with -integral groups
A. S. Detinko, D. L. Flannery, A. Hulpke
We generalize our methodology for computing with Zariski dense subgroups of and , to accommodate input dense subgroups …
Freeness and -arithmeticity of rational Möbius groups
A. S. Detinko, D. L. Flannery, A. Hulpke
We initiate a new, computational approach to a classical problem: certifying non-freeness of (-generator, parabolic) Möbius subgroups of . The main to…
Locally nilpotent linear groups
A. S. Detinko, D. L. Flannery
We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q…
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…
Algorithms for the Tits alternative and related problems
A. S. Detinko, D. L. Flannery, E. A. O'Brien
We present an algorithm that decides whether a finitely generated linear group over an infinite field is solvable-by-finite: a computationally effective version of the Tits alterna…
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…
Algorithms for linear groups of finite rank
A. S. Detinko, D. L. Flannery, E. A. O'Brien
Let be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of and a bound on the Prüfer rank of . This yields…
Integrality and arithmeticity of solvable linear groups
W. A. de Graaf, A. S. Detinko, D. L. Flannery
We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group is arithmetic. This incorporates a procedure to compute a generat…
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…
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…