相关论文: Dual Ore's theorem on distributive intervals of fi…

Boij-S\"oderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring $S = k[x_1, \ldots, x_n]$. We posit that a similar combinatorial description can be given for…

We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…

The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…

I prove the group theory analogues of some Lie and Leibniz algebra results on F-hypercentral and F-hypereccentric modules.

Let $p$ be a prime and $G$ a subgroup of $GL_d(p)$. We define $G$ to be $p$-exceptional if it has order divisible by $p$, but all its orbits on vectors have size coprime to $p$. We obtain a classification of $p$-exceptional linear groups.…

It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatoric group and its subgroups.

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…

We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.

We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular graphs, among regular graphs in terms of the eigenvalues and the…

We prove a version of uniqueness theorem for Cuntz-Pimsner algebras of discrete product systems over semigroups of Ore type. To this end, we introduce Doplicher-Roberts picture of Cuntz-Pimsner algebras, and the semigroup dual to a product…

We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of…

The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using…

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also…

It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local…

Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…

In this article, we shall generalize a theorem due to Frobenius in group theory, which asserts that if $p$ is a prime and $p^{r}$ divides the order of a finite group, then the number of subgroups of order $p^{r}$ is $\equiv$ 1(mod $p$).…

The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born…