Related papers: Boundedly simple groups of automorphisms of trees

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least…

We prove that the Picard group of a regular simply connected variety over an algebraically closed field of arbitrary characteristic is finitely generated. The main difficulty to overcome is the unavailability of resolution of singularities.…

A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index,…

We prove here that with a very small number of exceptions, when $G$ is a sporadic simple group and $p$ is a prime such that the Sylow $p$-subgroups of $G$ are nonabelian, then $Out(G)$ is isomorphic to the outer automorphism groups of the…

The paper follows two interconnected directions. 1. Let $G$ be a Roelcke precompact closed subgroup of the group $\Sym(\omega)$ of permutations of the natural numbers. Then $\Inn(G)$ is closed in $\Aut(G)$, where $\Aut(G)$ carries the…

Let $R_m$ be the (unique) universal homogeneous $m$-edge-coloured countable complete graph ($m\ge2$), and $G_m$ its group of colour-preserving automorphisms. The group $G_m$ was shown to be simple by John Truss. We examine the automorphism…

Let $K$ be an algebraically closed field of arbitrary characteristic and let $X$ be an irreducible projective variety over $K$. Let $G\subseteq\text{Bir}(X)$ be a bounded-degree subgroup. We prove that there exists an irreducible projective…

We prove that every simple polygon contains a degree 3 tree encompassing a prescribed set of vertices. We give tight bounds on the minimal number of degree 3 vertices. We apply this result to reprove a result from Bose et al. that every set…

We consider branched coverings which are simple in the sense that any point of the target has at most one singular preimage. The cobordism classes of $k$-fold simple branched coverings between $n$-manifolds form an abelian group…

We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups $G$, finding a sufficient condition for $G$ to have more than one end in terms of its…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i),…

A subgroup $H$ of a group $G$ is confined if the $G$-orbit of $H$ under conjugation is bounded away from the trivial subgroup in the space $\operatorname{Sub}(G)$ of subgroups of $G$. We prove a commutator lemma for confined subgroups. For…

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…

A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…

This article gives the proof of results announced in [J. Blanc, Finite Abelian subgroups of the Cremona group of the plane, C.R. Acad. Sci. Paris, S\'er. I 344 (2007), 21-26.] and some description of automorphisms of rational surfaces.…

We study closed subgroups $G$ of the automorphism group of a locally finite tree $T$ acting doubly transitively on the boundary. We show that if the stabiliser of some end is metabelian, then there is a local field $k$ such that…

It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold with finite number of ends are bounded. It follows that these groups are uniformly perfect. In order to characterize the…

We prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer…