Related papers: Finite group characters on free resolutions

This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…

For modules over group rings we introduce the following numerical parameter. We say that a module A over a ring R has finite r-generator property if each f.g. (finitely generated) R-submodule of A can be generated exactly by r elements and…

We present a procedure that constructs, in a combinatorial manner, a chain complex of free modules over a polynomial ring in finitely many variables, modulo an ideal generated by quadratic monomials. Applying this procedure to two specific…

We survey some results concerning finite group actions on products of spheres.

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…

Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\A(F_n)$ arising through the action of finite index subgroups of it on…

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…

We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.

Let $Q=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with the standard $N^n$-grading. Let $\phi$ be a morphism of finite free $N^n$-graded $Q$-modules. We translate to this setting several notions and constructions that appear…

In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two…

We find a lower bound to the size of finite groups detecting a given word in the free group, more precisely we construct a word w_n of length n in non-abelian free groups with the property that w_n is the identity on all finite quotients of…

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

There has been some interest on how the average character degree affects the structure of a finite group. We define, and denote by $ \mathrm{anz}(G) $, the average number of zeros of characters of a finite group $ G $ as the number of zeros…

We construct free resolutions for quotient rings $R/\langle \mathcal{I}', \mathcal{I}\mathcal{J}, \mathcal{J}'\rangle$, give conditions for the quotient to be realized as a fiber product, and give criteria for the construction to be…

Minimal free resolutions of graded modules over a noetherian polynomial ring have been attractive objects of interest for more than a hundred years. We introduce and study two natural extensions in the setting of graded modules over a…

This paper gives a sharp upper bound for the Betti numbers of a finitely generated multigraded $R$-module, where $R=\Bbbk [x_{1},...,x_{m}]$ is the polynomial ring over a field $\Bbbk$ in $m$ variables. The bound is given in terms of the…