相关论文: Elementary equivalence of stable linear groups ove…

We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results concern two cases: saturated PAC structures and non-saturated…

The paper is devoted to model-theoretic properties of Kac-Moody groups with the focus on elementary equivalence of Kac-Moody groups. We show that elementary equivalence of (untwisted) affine Kac-Moody groups implies coincidence of their…

In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.

In this paper we give a necessary and sufficient combinatorial condition for a monomial ideal to have a linear resolution over fields of characteristic 2. We also give a new proof of Fr\"oberg's theorem over fields of characteristic 2.

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We prove the linkage principle and describe blocks of the general linear supergroups $GL(m|n)$ over the ground field $K$ of characteristic $p\neq 2$.

We prove that, except for a few cases, stable linearizability of finite subgroups of the plane Cremona group implies linearizability.

This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

It is proved that (elementary) Chevalley groups $G_\pi (\Phi,K)$ and $G_{\pi'}(\Phi',K')$ (or $E_\pi (\Phi,K)$ and $E_{\pi'}(\Phi',K'))$ over infinite fields $K$ and $K'$ of characteristics $\ne 2$, with weight lattices $\Lambda$ and…

In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as $GL_n(F), SL_n(F)$ and $T_n(F)$ over a field $F$ provided $n \geq 3$.

We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.

We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the…

We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.

Our aim in this paper is to prove in the setting of Kato-Milne cohomology in characteristic 2 an exact sequence which is analogue to the Milnor-Scharlau sequence [8, Theorem 6.2]. This is an extension of the Milnor exact sequence proved in…

This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…

We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.

In this note we give a characterization of elementary abelian 2-groups in terms of their maximal sum-free subsets.