Generating random elements in finite groups.
Grouptheoretical investigations on computers
Idempotent-generated subsemigroups of the symmetric semigroup of degree four: computer investigations.
Irreducible cyclic presentations of the trivial group.
Looking for identities on a bicyclic semigroup with computer assistance.
Machine calculations in Weyl groups.
On Integral Groups. I. The Reducible Case.
On Integral Groups. II. The Irreducible Case.
Presentations of finite simple groups: a computational approach
All finite simple groups of Lie type of rank over a field of size , with the possible exception of the Ree groups , have presentations with at most 49 relations and bit-length . Moreover, and have presentations with 3 generators; 7 relations and bit-length , while has a presentation with 6 generators, 25 relations and bit-length .
Product replacement in the Monster.
Recherche des graphes des matrices de Coxeter hyperboliques d’ordre
Representing subgroups of finitely presented groups by quotient subgroups.
Right division in Moufang loops
If is a group, and the operation is defined by then by direct verification is a quasigroup which satisfies the identity . Conversely, if one starts with a quasigroup satisfying the latter identity the group can be constructed, so that in effect is determined by its right division operation. Here the analogous situation is examined for a Moufang loop. Subtleties arise which are not present in the group case since there is a choice of defining identities and the identities produced by...
Simple groups in computational group theory.
Standard generators for .
Testing Cayley graph densities
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an -generated group is amenable if and only if the density of the corresponding Cayley graph equals to . We test amenable and non-amenable...
The groups of order at most 2000.
Über ein Programm zur Berechnung der Automorphismengruppe einer endlichen Gruppe.
Utilisation d'APL pour calculer des monoïdes finis
Графическое построение собирательной формулы для некоторых типов групп