Related papers: Finite Groups of Essential Dimension 2

In this paper, we classify all finite groups $G$ which have the following property: for all subsets $A \subseteq G$, we have $|AA^{-1}| = |A^{-1}A|$. This question is motivated by the problem in additive combinatorics of More Sums Than…

A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also…

In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.

We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide explicit bounds for orders of finite subgroups of automorphism groups of…

The category of linear algebraic groups admits non-surjective epimorphisms. For simple algebraic groups of rank $2$ defined over algebraically closed fields, we show that the minimal dimension of a closed epimorphic subgroup is $3$.

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…

In this article we classify all $L_9$-free finite groups.

We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.

The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…

Let $k$ be a field of arbitrary characteristic. Let $S$ be a singular surface defined over $k$ with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation $\tilde{S}$ is finite dimensional.…

We characterize those valued fields for which the image of the valuation ring under every polynomial in several variables contains an element of maximal value, or zero.

We construct the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over compact discrete valuation rings of even residual characteristic. We also prove that the complex group algebras of $\mathrm{SL}_2$ over finite…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose…

A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…

We classify closed abelian subgroups of the simple groups $G_2$, $F_4$, $Aut(so(8))$ having centralizer the same dimension as the dimension of the subgroup, as well as finite abelian subgroups of certain spin and half-spin groups having…

We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…

This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.