Related papers: Primitive pairs of K-groups

We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the problem to primitive actions of almost simple groups of Lie…

We review some recent results on $K$-theory of perfection of commutative $\mF_p$-algebras and provide an alternative proof.

In this short note we answer to a question of group theory from arXiv:0910.5080. In that paper the author describes the set of realizable Steinitz classes for so-called $A'$-groups of odd order, obtained iterating some direct and semidirect…

Let A be a commutative noetherian ring. Call a functor <<commutative A-algebras>> --> <<sets>> coherent if it can be built up (via iterated finite limits) from functors of the form B \mapsto M tensor_A B, where M is a f.g. A-module. When…

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

For certain negative rational numbers k, called singular values, and associated with the symmetric group S_N on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when the parameter equals k. It was shown by…

In this paper we compute the Galois cohomology of the pro-p completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in the 3-sphere whose linking number diagram is irreducible modulo p (e.g.…

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_1$-functor without using the corresponding result from linear $K$-theory under the…

For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S^3, such a sequence of polynomials arises naturally as the orders of certain…

We investigate properties of the formula $p \to \Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $\phi \to \Box\phi / \phi, \neg\phi$, and as a consequence, we obtain various…

Let $E/\mathbb{Q}$ be an elliptic curve, $p$ a prime and $K_{\infty}/K$ the anticyclotomic $\mathbb{Z}_p$-extension of a quadratic imaginary field $K$ satisfying the Heegner hypothesis. In this paper we make a conjecture about the fine…

We study the difference between the number of primitive roots modulo $p$ and modulo $p+k$ for prime pairs $p,p+k$. Assuming the Bateman-Horn conjecture, we prove the existence of strong sign biases for such pairs. More importantly, we prove…

In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and S\'{a}rk\"{o}zy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by a related conjecture of S\'{a}rk\"{o}zy, we prove…

This article, complement to the article [Que], deals with some generalizations of Futw\"angler's theorems for the second case of Fermat's Last Theorem (FLT2). Let $p$ be an odd prime, $\zeta$ a $p$th primitive root of unity, $K:=\Q(\zeta)$…

We develop the local-global theory of blocks for profinite groups. Given a field $k$ of characteristic $p$ and a profinite group $G$, one may express the completed group algebra $k[[G]]$ as a product $\prod_{i\in I}B_i$ of closed…

We prove a pro-$p$ version of Sela's theorem stating that a finitely generated group is $k$-acylindrically accessible. This result is then used to prove that $\mathrm{PD}^n$ pro-$p$ groups admit a unique $k$-acylindrical JSJ-decomposition.

Let G be a simple complex algebraic group and let K be a reductive subgroup of G such that the coordinate ring of G/K is a multiplicity free G-module. We consider the G-algebra structure of C[G/K], and study the decomposition into…

We introduce the Primitive Eulerian polynomial $P_{\cal A}(z)$ of a central hyperplane arrangement ${\cal A}$. It is a reparametrization of its cocharacteristic polynomial. Previous work of the first author implicitly show that, for…

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…

Let $K$ be a number field, and let $G\subset K^\times$ be a finitely generated subgroup. Fix some prime number $\ell$, and consider the set of primes $\mathfrak{p}$ of $K$ satisfying the following property: the reduction of $G$ modulo…