Timoshenko, E. I.
Published in
Mathematical Notes

Automorphisms of a partially commutative metabelian group SΓ defined by a finite simple graph Γ with r vertices are considered. The monoid P of matrices of order r is equipped with a congruence ≈. It is proved that the group of automorphisms acting identically on the quotient group by the commutator subgroup SΓ/[SΓ,SΓ] is isomorphic to the quotient...

Guirardel, Vincent Levitt, Gilbert

We study automorphisms of a relatively hyperbolic group G. When G is one-ended, 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 GL_n(Z) fixing certain basis elements. When ...

Shevelin, M. A.
Published in
Siberian Mathematical Journal

Let Fr be a free Lie algebra over the field ℂ. We give an example of some subgroup of Aut Fr that is isomorphic to a subgroup of ℂ* but not conjugated with a subgroup of the linear automorphism group. Some questions are formulated.

Ben Yaacov, Itaï Kaïchouh, Adriane

We extend Ahlbrandt and Ziegler's reconstruction results to the metric setting: we show that separably categorical metric structures are determined, up to bi-interpretability, by their automorphism groups.

Cara, P. Rottey, S. Van de Voorde, G.
Published in
Advances in Geometry

A linear representation T*n(K) of a point set K is a point-line geometry, embedded in a projective space PG(n+1; q), where K is contained in a hyperplane. We put constraints on K which ensure that every automorphism of T*n(K) is induced by a collineation of the ambient projective space. This allows us to show that, under certain conditions, two lin...

Kishimoto, Takashi Prokhorov, Yuri Zaidenberg, Mikhail

In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In contrast, we show in this note that for a del Pezzo surface Y of degree at most 2 the generaliz...

Kudaĭbergenov, K. Zh.
Published in
Siberian Advances in Mathematics

We obtain results on existence of dense free subgroups of the automorphism group of a homogeneous model.

Thas, Koen

We explain how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F-1) to a so-called "loose graph" (which is a generalization of a graph). Several properties of the Deitmar scheme can be proven easily from the combinatorics of the (loose) graph, and it also appears that known realizations of ob...

KISHIMOTO, TAKASHI PROKHOROV, YURI ZAIDENBERG, MIKHAIL
Published in
Transformation Groups

An affine algebraic variety X is called cylindrical if it contains a principal Zariski dense open cylinder U ≃ Z × A1. A polarized projective variety (Y, H) is called cylindrical if it contains a cylinder U = Y \ supp D, where D is an effective Q-divisor on Y such that [D] ∈ Q+[H] in PicQ(Y ). We show that cylindricity of a polarized projective var...

Makhnev, A. A. Paduchikh, D. V. Tsiovkina, L. Yu.
Published in
Siberian Mathematical Journal

Let Γ be an edge-symmetric distance-regular covering of a clique. Then the group G = Aut(Γ) acts twice transitively on the set Σ of antipodal classes. We propose a classification for the graphs based on the description of twice transitive permutation groups. This program is realized for a1 = c2. In this article we classify graphs in the case when t...