Related papers: Another definition of Euler class group of a Noeth…

There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)

A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible…

We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

We formulate and prove the Siegel-Weil formula for loop groups.

There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…

We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated…

We compute Euler characteristics of p-subgroup categories of finite groups

The aim of this article is to draw attention towards various natural but unanswered questions related to the lower central series of the unit group of an integral group ring.

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.

The definition of Suzuki groups over rings is given by means of an explicit description as a difference-algebraic group. For a (not necessarily perfect) field with more than two elements this construction produces a simple group.

The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of…

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.

The best known method to give a lower bound for the Noether number of a given finite group is to use the fact that it is greater than or equal to the Noether number of any of the subgroups or factor groups. The results of the present paper…

The exact value of the separating Noether number of an arbitrary finite abelian group of rank two is determined. This is done by a detailed study of the monoid of zero-sum sequences over the group.

The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this…

We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.