Transitive Subsemigroups of the Moebius Group

Subsemigroups of transitive semigroups

Let Γ be a topological semigroup acting on a topological space X, and let Γ0 be a subsemigroup of Γ. We give general conditions ensuring that Γ and Γ0 have the same transitive points.

Transitive Group Actions

Every action of a group on a set decomposes the set into orbits. The group acts on each of the orbits and an orbit does not have sub-orbits (unequal orbits are disjoint), so the decomposition of a set into orbits could be considered as a “factorization” of the set into “irreducible” pieces for the group action. Our focus here is on these irreducible parts, namely group actions with a single orbit.

Transitive Factorizations in the Hyperoctahedral Group

The classical Hurwitz Enumeration Problem has a presentation in terms of transitive factorisations in the symmetric group. This presentation suggests a generalization from type A to other £nite re¤ection groups and, in particular, to type B. We study this generalization both from a combinatorial and a geometric point of view, with the prospect of providing a means of understanding more of the s...

Subsemigroups of the Bicyclic Monoid

In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determin...

Regular Subgroups of a Transitive Substitution Group.