Related papers: Parabolic subgroups inside parabolic subgroups of …

We determine explicitly the structure of the automorphism group of a parabolic Inoue surface. We also describe the quotients of the surface by typical cyclic subgroups of the automorphism group.

Let $G$ be a $p$-adic reductive group. We determine the extensions between admissible smooth mod $p$ representations of $G$ parabolically induced from supersingular representations of Levi subgroups of $G$, in terms of extensions between…

The aim of this note is to prove that the parabolic closure of any subset of a Coxeter group is a parabolic subgroup. To obtain that, several technical lemmas on the root system of a parabolic subgroup are established.

In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\gam$, we produce a new graph through a purely combinatorial procedure, and call it the extension graph $\gam^e$ of…

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given…

By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate this phenomenon for quaternionic reflection groups. Here, in…

We find necessary and sufficient conditions for $P$-equivalence of arbitrary matrices and $P$-congruence of symmetric and alternating matrices, where $P$ is standard parabolic subgroup of $GL_n(F)$ and $F$ is an arbitrary field.

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show…

We prove that every subnormal subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent…

Given a Chevalley group ${\mathbf G}(q)$ and a parabolic subgroup $P\subset {\mathbf G}(q)$, we prove that for any set $A$ there is a certain growth of $A$ relatively to $P$, namely, either $AP$ or $PA$ is much larger than $A$. Also, we…

Using a probabilistic argument we show that the second bounded cohomology of an acylindrically hyperbolic group $G$ (e.g., a non-elementary hyperbolic or relatively hyperbolic group, non-exceptional mapping class group, ${\rm Out}(F_n)$,…

We describe the autotopism group Atp(G) of any abelian group G as being a semidirect product of its automorphism group Aut(G) and G^2. We then provide the subgroup structure of Atp(G) when G is a finite cyclic group.

One can observe that Coxeter groups and right-angled Artin groups share the same solution to the word problem. On the other hand, in his study of reflection subgroups of Coxeter groups Dyer introduces a family of groups, which we call Dyer…

In this paper, we define the 2-complete Artin complex and show that it is systolic for locally reducible Artin groups. The stabilizers of simplices in this complex are exactly the proper parabolic subgroups which are "2-complete." We use…

If $G$ is a finite primitive complex reflection group, all reflection subgroups of $G$ and their inclusions are determined up to conjugacy. As a consequence, it is shown that if the rank of $G$ is $n$ and if $G$ can be generated by $n$…

We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…

Let S 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 S, which we call canonical parabolic subgroups. A natural extension of the definition…

Baker and Riley proved that a free group of rank 3 can be contained in a hyperbolic group as a subgroup for which the Cannon-Thurston map is not well-defined. By using their result, we show that the phenomenon occurs for not only a free…

Let $\ell$ be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an $\ell$-Sylow subgroup.…

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…