Related papers: A note regarding some generalization of a Schur's …

We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…

This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.

In (Borceux-Janelidze 2001) they prove a Categorical Galois Theorem for ordinary categories, and establish the main result of (Joyal-Tierney 1984), along with the classical Galois theory of Rings, as instances of this more general result.…

Let $\gamma_i(G)$ and $Z_i(G)$ denote the $i$-th terms of the lower and upper central series of a group $G$, respectively. P. Hall showed that if $\gamma_{i+1}(G)$ is finite then the index $|G:Z_{2i}(G)|$ is finite. We prove that the same…

We compute the class group of a full rank upper cluster algebra in terms of its exchange polynomials. As a corollary, we recover a theorem by Cao, Keller, and Qin from 2023 characterizing the UFDs among these algebras. Furthermore, under…

We prove two conjectures of E. Khukhro and P. Shumyatsky concerning the Fitting height and insoluble length of finite groups. As a by-product of our methods, we also prove a generalization of a result of Flavell, which itself generalizes…

We prove a new upper bound on the essential p-dimension of the projective linear group PGLn.

The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called $C$-sets. The…

This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic 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.

This is the written version of the Bourbaki seminar given in January 2013 and published in 2014 (modulo an additional early reference added subsequently). It describes the first construction of infinite, finitely generated amenable simple…

The complete algebraic structure of semisimple finite group algebra of a generalized strongly monomial group is provided. This work extends the work of Broche and del R{\'{\i}}o on strongly monomial groups. The theory is complimented by an…

As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

A finite family $\mathrsfs{F}$ of subsets of a finite set $X$ is union-closed whenever $f,g\in\mathrsfs{F}$ implies $f\cup g\in\mathrsfs{F}$. These families are well known because of Frankl's conjecture. In this paper we developed further…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

Nearly twenty years ago Isaacs and the first author of this paper wrote a series of articles \cite{isa2}, \cite{da3}, \cite{da2} about what were called ``stabilizer limits'' of group characters, following the terminology of Berger…

We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.

We study some subgroups of the group of unitriangular automorphisms $U_n$ of a free associative algebra over a field of characteristic zero. We find the center of $U_n$ and describe the hypercenters of $U_2$ and $U_3$. In particular, we…

P. Frankl and J. Pach proved the following uniform version of Sauer's Lemma. Let $n,d,s$ be natural numbers such that $d\leq n$, $s+1\leq n/2$. Let $\cF \subseteq {[n] \choose d}$ be an arbitrary $d$-uniform set system such that $\cF$ does…