Related papers: On the maximality of the triangular subgroup

We study subgroups and quotients of outer automorphism groups of right-angled Artin groups (RAAGs). We prove that for all RAAGS, the outer automorphism group is residually finite and, for a large class of RAAGs, it satisfies the Tits…

In this paper, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds. Specifically, we prove that there exist 20…

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup of Aut(S) generated by all its algebraic subgroups is not generated by any countable family of such subgroups,…

Let $X$ be a compact Riemann surface of genus $g\geq 2$. Let $Aut(X)$ be its group of automorphisms and $G\subseteq Aut(X)$ a subgroup. Sharp upper bounds for $|G|$ in terms of $g$ are known if $G$ belongs to certain classes of groups, e.g.…

A coaction d of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A times_d G times_{d hat} G onto A otimes K(L^2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are…

We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano…

For any choice of a basis $\cal A$ the free group $F_N$ of finite rank $N \geq 2$ can be canonically identified with the set $F(\cal A)$ of reduced words in $\cal A\cup \cal A^{-1}$. However, such a word $w \in F(\cal A)$ admits a second…

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

A polynomial automorphism of $\mathbb{A}^n$ over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms, including…

Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over…

We show that for any $n\geq5$ there exist connected algebraic subgroups in the Cremona group $\mathrm{Bir}(\mathbb{P}^n)$ that are not contained in any maximal connected algebraic subgroup. Our approach exploits the existence of stably…

We study properties of the realizations of groups as the combinatorial automorphism group of a convex polytope. We show that for any non-abelian group $G$ with a central involution there is a centrally symmetric polytope with $G$ as its…

A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\leftthreetimes P,$ where $G$ is a compact…

We prove that for any transitive subshift $X$ with word complexity function $c_n(X)$, if $\liminf \frac{\log (c_n(X)/n)}{\log \log \log n} = 0$, then the quotient group $\textrm{Aut}(X,\sigma) / \langle \sigma\rangle$ of the automorphism…

Let $G$ be a simple algebraic group of adjoint type over the field $\mathbb{C}$ of complex numbers, $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G.$ In this article, we show that $\alpha$ is a co-minuscule root if and…

We study the maximal rigid subcategories in $2-$CY triangulated categories and their endomorphism algebras. Cluster tilting subcategories are obviously maximal rigid; we prove that the converse is true if the $2-$CY triangulated categories…

We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we…

Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not…

Let $F_n$ be the free group of rank $n$, and let $\rho_{ab}:\mathrm{Aut}(F_n)\to \mathrm{GL}_n(\mathbb Z)$ be the map induced by the natural projection $F_n\to\mathbb Z^n$. It is a long-standing open problem whether the subgroup of…

In universal algebraic geometry the category of the finite generated free algebras of some fixed variety of algebras and the quotient group A/Y are very important. Here A is a group of all automorphisms of this category and Y is a group of…