Related papers: On Some Algebraic Properties of Generalized Groups
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.
A group element is called generalized torsion if a finite product of its conjugates is equal to the identity. We show that in a finitely generated abelian-by-finite group, an element is generalized torsion if and only if its image in the…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
We first prove Bosch-L\"utkebohmert-Raynaud's conjectures on existence of global N\'eron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the…
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…
The notion of the holomorph of a generalized Bol loop and generalized flexible-Bol loop are characterized. With the aid of two self-mappings on the holomorph of a loop, it is shown that: the loop is a generalized Bol loop if and only if its…
We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL_2(5) is a Beauville group. In particular, we settle a…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing…
The conjecture that semi-p-abelian groups is strongly semi-p-abelian is flase for p=3.And it's true for metabelian semi-p-abelian groups.
We introduce and develop a structure theory of a new class of noncommutative rings - Galois orders, that generalize classical orders in noncommutative rings. Galois orders realized as certain subrings of invariants in skew semigroup rings.…
We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We present results about groupoids of small order with Bol-Moufang type identities both classical and non-classical which are listed in [7, 8].
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
We extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global…
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…
For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…