Related papers: Rank 3 Bingo

We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…

The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.

In this paper we study powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of powerful 3-Engel groups and the subclass of powerful metabelian 3-Engel groups.

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three.

We give a classification of ordered five points in $\mathbb P^3$ under the diagonal action of $GL_4$ over an algebraically closed field of characteristic $0$, by an explicit description of the diagonal action of $GL_4$ on the quintuple of…

We show that the Cantor-Bendixson rank of a limit group is finite as well as that of a limit group of a linear group.

We classify finite-dimensional complex Hopf algebras $A$ which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements $G(A)$ is abelian such that all prime divisors of the order…

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…

We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate…

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_\lambda, 0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete invariant. This…

For every finite abelian group $A$ and $n\geq 3$, we construct a finitely presented group defined by explicit generators and relations, such that its center is $\pi_n(\Sigma K(A,1))$.

We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new…

Let $X/\mathbb{F}_{q}$ be a smooth geometrically connected variety. Inspired by work of Corlette-Simpson over $\mathbb{C}$, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on $X$ come from…

We prove global rigidity results for some linear abelian actions on tori. The type of actions we deal with includes in particular maximal rank semisimple actions on $\T^N$.

We give Scott sentences for certain computable groups, and we use index set calculations as a way of checking that our Scott sentences are as simple as possible. We consider finitely generated groups and torsion-free abelian groups of…

In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic $\mathbb{Z}^d$-actions given by Schmidt using…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

We investigate bounds on the dimension of cohomology groups for finite groups acting on an irreducible kG-module for G a finite group of bound sectional p-rank and k an algebraically closed field of characteristic p.