3 citations · 6 across the 4 of their papers we have counts for
8 papers · 1 filter
The perfect groups of order up to two million
Alexander Hulpke
We enumerate the 15768 perfect groups of order up to , up to isomorphism, thus also completing the missing cases in the prior classification. The work supplements the…
Calculating Subgroups with GAP
Alexander Hulpke
We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP
Universal Covers of Finite Groups
Heiko Dietrich, Alexander Hulpke
Motivated by quotient algorithms, such as the well-known -quotient or solvable quotient algorithms, we describe how to compute extensions of a finite group by a d…
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…
Constructive Membership Tests in Some Infinite Matrix Groups
Alexander Hulpke
We describe algorithms and heuristics that allow us to express arbitrary elements of SLn (Z) and Sp2n (Z) as products of generators in particular "standard" generating sets. For el…
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…