Related papers: On the local-indicability Cohen-Lyndon Theorem

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

In the homology cobordism group $\Theta_\mathbb{Z}^3$, it is not known if there are non-trivial linear dependences between Seifert fibered spheres. Based on involutive Heegaard Floer theory, Hendricks, Manolescu, and Zemke introduced the…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved by Dikranjan, Goldsmith, Salce and Zanardo. It was later extended by Shlossberg to torsion nilpotent groups of class 2. As our main…

If T is an ergodic automorphism of a Lebesgue probability space (X,A,m), the set of coboundries B = db =T(b)+b with symmetric difference + form a subgroup of the set of cocycles A. Using tools from descriptive set theory, Greg Hjorth showed…

Generalising Solomon's theorem, C. Gordon and F. Rodriguez-Villegas have proven recently that, in any group, the number of solutions to a system of coefficient-free equations is divisible by the order of this group whenever the rank of the…

We present an algorithm to decide whether or not a finitely generated subgroup of the isometry group of a locally finite simplicial tree is both discrete and free. The correctness of this algorithm relies on the following conjecture: every…

For an element $w$ of the simply-laced Weyl group, Buan-Iyama-Reiten-Scott defined a subcategory $\mathcal{F}(w)$ of a module category over a preprojective algebra of Dynkin type. This paper aims at studying categorical properties of…

In [20] Esnault asked whether on a general quotient surface singularity the rank and the first Chern class distinguish isomorphism classes of indecomposable reflexive modules. Wunram gave a contraexample in [46] showing two different full…

We prove that if $S$ is an $E$-solid locally inverse semigroup, and $\rho$ is an inverse semigroup congruence on $S$ such that the idempotent classes of $\rho$ are completely simple semigroups then $S$ is embeddable into a…

We first prove that the Whitehead group of a torsion-free virtually solvable linear group vanishes. Next we make a reduction of the fibered isomorphism conjecture from virtually solvable groups to a class of virtually solvable Q-linear…

In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of $C^*$-algebras, after tensoring with $\mathbb{Q}$, by…

The canonical trace on the reduced C*-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C^*-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the…

This paper considers the following conjecture: If $R$ is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal $J$ generated by a system of parameters, the Chern coefficient…

The local H theorem is shown to hold for the Enskog equation with a modified Enskog factor proposed by the authors [Phys. Rev. E 111, 065108 (2025)]. This is a stronger statement than the global one in the same paper and has been obtained…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the…

The Burns-Hale theorem states that a group G is left-orderable if and only if G is locally projectable onto the class of left-orderable groups. Similar results have appeared in the literature in the case of UPP groups and Conradian…

Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. If $X$ is Dieudonn\'{e} complete (for example, metrizable), then $L(X)$ is a reflexive group if and only if $X$ is discrete. Answering a question posed in [9] we prove…

Let F be a local henselian nonarchimedean field of residual field k, and let G be the group of F-points of a connected reductive group defined over F. It is well-known that the quotient of any parahoric subgroup of G by its first congruence…

Let $\mathbb{F}_q$ be a finite field with $q = p^s$ elements. Let $V$ be a $d$ dimensional vector space over $\mathbb{F}_q$ and let $G$ be a subgroup of $GL(V)$. Let $R = \mathbb{F}_q[V] = \text{Sym}_{\mathbb{F}_q}(V^*)$ and let $G$ act…