We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.

The finite generation of the ring of invariants of a special class of unipotent groups is established-namely, unipotent radicals of parabolic subgroups.

In this paper we calculate the parabolic class number of subgroups of Hecke groups H( √ 2),H( √ 3). Subject Classification: 20 G-H

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such do not lie inside proper parabolic unless possibly when their connected component is torus. This extends the earlier Testerman and Zalesski treating subgroups.

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers sat...

In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic subgroup. As a corollary, we construct subgroups of the mapping class group (for all genus at least 2), which are isomorphic to non-abelian closed surface groups i...

We study invariant random subgroups (IRSs) of semidirect products G = AoΓ. In particular, we characterize all IRSs of parabolic subgroups of SLd(R), and show that all ergodic IRSs of Rdo SLd(R) are either of the form RdoK for some IRS of SLd(R), or are induced from IRSs of Λo SL(Λ), where Λ < Rd is a lattice.

We study automorphisms of a relatively hyperbolic group G. When G is oneended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups of GLn(Z) fixing certain basis elements. When more general parabolic groups are allowed, these ...

We determine the nature of the fixed point sets of groups of order p, acting on complexes of distinguished p-subgroups (those p-subgroups containing pcentral elements in their centers). The case when G has parabolic characteristic p is analyzed in detail.