Related papers: Another definition of Euler class group of a Noeth…
We will study the Euler class group of a commutative Noetherian ring $A$ of dimension $d$, developed by S.M. Bhatwadekar and Raja Sridharan. This is my M.Phil thesis from 2001.
The exact degree bound for the generators of rings of polynomial invariants is determined for the finite, non-cyclic groups having a cyclic subgroup of index two. It is proved that the Noether number of these groups equals one half the…
This is an exposition of the homological classification of actions of surface groups on the plane, in every degree of smoothness.
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
The groups distinguish their von Neumann algebras, in the case when these are factors.
We define the notion of the orbit group of a quandle via its connectivity and compute the orbit groups for some basic quandles. We also show that the orbit group counts the number of orbits of certain quandles.
The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.
The exact value of the separating Noether number of some finite abelian groups is determined, including the direct sums of cyclic groups of the same order.
The finite groups having an indecomposable polynomial invariant whose degree is at least half of the order of the group are classified. Apart from four sporadic exceptions these are exactly the groups having a cyclic subgroup of index at…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
Let R be a Noetherian commutative ring of dimension n >2 and let A=R[T,T^{-1}]. Assume that the height of the Jacobson radical of R is atleast 2. Let P be a projective A-module of rank n=dim A - 1 with trivial determinant. We define an…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
Topological characterization of torus groups is given.
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
An $S$-ring (Schur ring) is called central if it is contained in the center of the group ring. We introduce the notion of a generalized Schur group, i.e. such finite group that all central $S$-rings over this group are schurian. It…
A finite group $G$ is called a Schur group if every $S$-ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of $\sym(G)$ that contains all right translations. We prove that every nonabelian nilpotent Schur group…
We define the $m$th-order Eulerian numbers with a combinatorial interpretation. The recurrence relation of the $m$th-order Eulerian numbers, the row generating function and the row sums of the $m$th-order Eulerian triangle are presented. We…
Consideration of certain properties of group rings and their ideals search
We establish the equality of two definitions of an Euler class in algebraic geometry: the first definition is as a "characteristic class" with values in Chow-Witt theory, while the second definition is as an "obstruction class." Along the…
Quasigroup equational definitions are given.