Related papers: On Schur Rings over Infinite Groups III

In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…

Following Wielandt, a finite group $G$ is called a $B$-group (Burnside group) if every primitive group containing a regular subgroup isomorphic to $G$ is doubly transitive. Using a method of Schur rings, Wielandt proved that every abelian…

We conjecture that if $G$ is a finite primitive group and if $g$ is an element of $G$, then either the element $g$ has a cycle of length equal to its order, or for some $r,m$ and $k$, the group $G\leq S_m\wr S_r$, preserving a product…

We present a method to explicitly compute a complete set of orthogonal primitive idempotents in a simple component with Schur index 1 of a rational group algebra $\mathbb{Q}G$ for $G$ a finite generalized strongly monomial group. For the…

Let $G$ be a cyclic $p$-group for some prime number $p>0$ and let $R$ be a complete discrete valuation ring in mixed characteristic. In this paper, we present a generalization of two results that characterize $RG$-permutation modules,…

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…

It has been proved in \cite{ge} for every $p$-group of order $p^n$, $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$, where $t(G)\geq 0$. In \cite{be, el, zh}, the structure of $G$ has been characterized for $t(G)=0,1,2,3$ by several authors.…

Let $F$ be any field of characteristic $p$. It is well-known that there are exactly $p$ inequivalent indecomposable representations $V_1,V_2,...,V_p$ of $C_p$ defined over $F$. Thus if $V$ is any finite dimensional $C_p$-representation…

This paper investigates the algebraic and graphical structure of the ring $\mathbb{Z}_{sp}$, with a focus on its decomposition into finite fields, kernels, and special subsets. We establish classical isomorphisms between $\mathbb{F}_s$ and…

Let $k$ be a perfect field and let $p$ be a prime number different from the characteristic of $k$. Let $C$ be a smooth, projective and geometrically integral $k$-curve and let $X$ be a Severi-Brauer $C$-scheme of relative dimension $p-1$ .…

We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…

We recall Schur's work on universal central extensions and develop the analogous theory for categorical extensions of groups. We prove that the String 2-groups are universal in this sense and study in detail their restrictions to the finite…

Let $E$ be the Fermat cubic curve over $\bar{\mathbb{Q}}$. In 2002, Schoen proved that the group $CH^2(E^3)/\ell$ is infinite for all primes $\ell\equiv 1\pmod 3$. We show that $CH^2(E^3)/\ell$ is infinite for all prime numbers $\ell> 5$.…

We extend the notion of free $p$-central groups for odd primes $p$ to the case $p=2$ by introducing a variant of the lower $p$-central series. This enables us to calculate Schur multipliers of free $p$-central groups. We also prove that for…

In this paper we study division algebras over the function fields of curves over $\Q_p$. The first and main tool is to view these fields as function fields over nonsingular $S$ which are projective of relative dimension 1 over the $p$ adic…

We initiate the study of profinite groups of non-negative deficiency. The principal focus of the paper is to show that the existence of a finitely generated normal subgroup of infinite index in a profinite group $G$ of non-negative…

Groups with a large $p$-subgroup, $p$ a prime, include almost all of the groups of Lie type in characteristic $p$ and so the study of such groups adds to our understanding of the finite simple groups. In this article we study a special…

A perfect isometry is an important relation between blocks of finite groups as many information about blocks are preserved by it. If we consider the group of all perfect isometries between a block to itself then this gives another…

Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…