Related papers: Finite Groups of Essential Dimension 2

Even though big mapping class groups are not countably generated, certain big mapping class groups can be generated by a coarsely bounded set and have a well defined quasi-isometry type. We show that the big mapping class group of a stable…

We prove that the function field of an algebraic variety of dimension greater than 1 over an algebraically closed field of characteristic zero is determined by its first and second Milnor K-groups.

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…

We classify finite groups with a small average number of zeros in the character table.

We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…

We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $p$-adic field of constant group schemes of rank two over finite fields, by counting the rational points of a…

Let k be an algebraically closed field of characteristic 0. We conclude the classification of finite dimensional pointed Hopf algebras whose group of group-likes is S_4. We also describe all pointed Hopf algebras over S_5 whose…

In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.

Let $G$ be a linear algebraic group over a field. We show that, under mild assumptions, in a family of primitive generically free $G$-varieties over a base variety $B$ the essential dimension of the geometric fibers may drop on a countable…

Suppose $G$ is a finite group and $p$ is either a prime number or $0$. For $p$ positive, we say that $G$ is weakly tame at $p$ if $G$ has no non-trivial normal $p$-subgroups. By convention we say that every finite group is weakly tame at…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.

We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.

In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete…

Let $\mathbb{F}_2^\omega$ denote the countably infinite dimensional vector space over the two element field and $\operatorname{GL}(\omega, 2)$ its automorphism group. Moreover, let $\operatorname{Sym}(\mathbb{F}_2^\omega)$ denote the…

In this note we describe the finite groups $G$ having $|G|-2$ cyclic subgroups. This partially solves the open problem in the end of \cite{3}.

We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential…

In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…