Related papers: Finite groups of birational transformations
We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
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…
In this note, finite type epimorphisms of rings are characterized.
We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.
This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.
We investigate finite and infinite nested square root formulas convergent to unity.
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…
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…
In this short note we study the cohomology algebra of saturated fusion systems using finite groups which realize saturated fusion systems and Hochschild cohomology of group algebras. A similar result to a theorem of Alperin is proved for…
It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.