Related papers: Cubic maps from the group of order $3$

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

We show that the definition of unipotent (resp. nilpotent) pieces for classical groups given by Lusztig (resp. Lusztig and the author) coincides with the combinatorial definition using closure relations on unipotent classes (resp. nilpotent…

We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $\Sigma^0_3$-complete. However, when we consider groups of infinite rank, it becomes $\Sigma^1_1$-complete,…

We study the \Q_p-unipotent Albanese map for curves over local fields with residue characteristic different from p and show that it has finite image. As a corollary, we deduce a simple `pi_1'-proof of Siegel's theorem for rank 1 elliptic…

We investigate the palindromic width of finitely generated solvable groups. We prove that every finitely generated $3$-step solvable group has finite palindromic width. More generally, we show the finiteness of palindromic width for…

We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex…

We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…

In an earlier work, finite groups whose power graphs are minimally edge connected have been classified. In this article, first we obtain a necessary and sufficient condition for an arbitrary graph to be minimally edge connected.…

A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fra\"iss\'e theory, we show that there is a universal ultrahomogeneous cubic space $V$ of countable infinite dimension, which is unique up to…

We have sorted the SmallGroups library of all the finite groups of order smaller than 2000 to identify the groups that possess a faithful three-dimensional irreducible representation (`irrep') and cannot be written as the direct product of…

Groups defined by presentations for which the components of the corresponding star graph are the incidence graphs of generalized polygons are of interest as they are small cancellation groups that - via results of Edjvet and Vdovina - are…

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

For an infinite group $G$, the poset $\mathcal{L}_G$ of group topologies constitutes a complete lattice. Although $\mathcal{L}_G$ is modular when $G$ is abelian, this property fails to persist for nilpotent groups. Extending Arnautov's 2010…

Let $\Sigma$ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal $k$--step nilpotent cover of…

We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and…

Collection of (equivariant) $\rm{PL}$-mappings admitting a relative abelian, cyclic, quaternionic, bicyclic, and quaternionic-cyclic structures are constructed.

Let $\Sigma_{g,n}$ be the orientable genus $g$ surface with $n$ punctures, where $2-2g-n<0$. Let $$\rho: \pi_1(\Sigma_{g,n})\to GL_m(\mathbb{C})$$ be a representation. Suppose that for each finite covering map $f: \Sigma_{g', n'}\to…

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular,…

In this paper we investigate Abel maps on normal surface singularities described in \cite{NNI}. We investigate the affine version of the class of the images of Abel maps on normal surface singularities. More precisely we consider the…

We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an…