Related papers: Normality theorem for elementary symplectic group …

A.A. Suslin proved a normality theorem for an elementary linear group and V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. We generalized the result…

We prove a normality theorem for the "true" elementary subgroups of $SL_n(A)$ defined by the ideals of a commutative unital ring $A$. Our result is an analogue of a normality theorem, due to Suslin, for the standard elementary subgroups,…

V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group…

A new set of elementary symplectic elements is described, It is shown that these also generate the elementary symplectic group {\rm ESp}$_{2n}(R)$. These generators are more symmetrical than the usual ones, and are useful to study the…

We deduce the relative version of the equivalences relating the relative Local Global Principle and the Normality of the relative Elementary subgroups of the traditional classical groups, viz. general linear, symplectic and orthogonal…

In this paper we deduce a graded version of Quillen--Suslin's Local-Global Principle for the traditional classical groups, viz. general linear, symplectic and orthogonal groups and establish its equivalence of the normality property of the…

Let $R$ be an exchange ring. We prove that the relative elementary subgroups $E_n(R,I)$ are normal in the general linear group $GL_n(R)$ if $n\geq 1$ and that the standard commutator formula $E_n(R,I)=[E_n(R),E_n(R,I)]=[E_n(R),C_n(R,I)]$…

Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of…

In this article, we prove commutativity principal for linear, symplectic and transvection groups. This principle is a consequence of Quillen-Suslin local global principle and using a non-symmetric application of it as done by A. Bak. The…

In [9] Bogdan Nica presented an elementary proof of a result which says that the relative elementary linear group with respect to a square of an ideal of the ring is a subset of the true relative elementary linear group. The original result…

In this article we define a set of matrices analogous to Vaserstein-type matrices which was introduced in the paper `Serre's problem on projective modules over polynomial rings and algebraic K-theory' by Suslin-Vaserstein in 1976. We prove…

The normal covering number $\gamma(G)$ of a finite, non-cyclic group $G$ is the least number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We prove that there is a positive constant $c$…

It is proved that any family of analytic functions with spherical derivative uniformly bounded away from zero ist normal.

We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius…

We show that Rojtman's theorem holds for normal schemes: For any reduced normal scheme of finite type over an algebraically closed field, the torsion of the zero'th Suslin homology group agrees with the torsion of the albanese variety (the…

We prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes $S$. Additionally, we obtain average sizes for the relaxed Selmer…

Let $\mathbb{A} = (A, \cdot)$ be a semigroup. We generalize some recent results by G. A. Freiman, M. Herzog and coauthors on the structure theory of set addition from the context of linearly orderable groups to linearly orderable…

We derive a Serre presentation of distribution algebras of loop groups in characteristic $p$ and apply it to give a new proof of the normality of Schubert varieties inside parahoric affine Grassmannians, for all connected reductive groups…

Szemeredi's regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemeredi's regularity lemma in the context of abelian groups and use it to derive some…