12 citations · 30 across the 19 of their papers we have counts for
10 papers · 1 filter
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…
2-generation of simple Lie algebras and free dense subgroups of algebraic groups
Alla S. Detinko, Willem A. de Graaf
We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are f…
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…