Machine calculations in Weyl groups.
Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and -manifold groups are malnormal.
Let B be a 3-dimensional handlebody of genus g. Let ℳ be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which ℳ acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation of ℳ.
In questo lavoro viene trovata un'espressione esplicita per i rappresentanti dei laterali di sottogrupi parabolici di gruppi di Coxeter aventi lunghezza minima: dato un sistema di Coxeter ed un suo sottogruppo parabolico , con , si determina esplicitamente in ogni laterale di un elemento avente lunghezza minima. Nella sezione 2 trattiamo i casi classici, i.e. , e . Dopo ciò, nella sezione 3, diamo una procedura per risolvere il problema nei restanti casi eccezionali, insieme a qualche...
We show that the class of groups which have monoid presentations by means of finite special -confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.
We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.