Related papers: A Restriction Theorem for M\'etivier Groups

In this paper, we investigate the $L^{p}$-boundedness of the Riesz means and the $L^{p_{1}}\times L^{p_{2}}\rightarrow L^{p}$ boundedness of the bilinear Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of…

Hardy's type uncertainty principle on connected nilpotent Lie groups for the Fourier transform is proved. An analogue of Hardy's theorem for Gabor transform has been established for connected and simply connected nilpotent Lie groups.…

We show that uniform approximate lattices in nilpotent Lie groups are subsets of model sets. This extends a theorem due to Yves Meyer about quasicrystals in Euclidean spaces. To do so we study relatively dense subsets of simply connected…

We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.

In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.

We extend the Siu--Beauville theorem to a certain class of compact Kaehler--Weyl manifolds, proving that they fiber holomorphically over hyperbolic Riemannian surfaces whenever they satisfy the necessary topological hypotheses. As…

We establish regularity conditions for $L_p$-boundedness of Fourier multipliers on the group von Neumann algebras of higher rank simple Lie groups. This provides a natural H\"ormander-Mikhlin criterion in terms of Lie derivatives of the…

The aim of the paper is to popularise nilpotent Lie groups (notably the Heisenberg group and alike) in the context of Clifford analysis and related models of mathematical physics. It is argued that these groups are underinvestigated in…

We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_G(H)$ of the complement is nilpotent of class $c$. It is proved that…

In this paper we extend some classical results of Convex Analysis to the sub-Riemannian setting of the Heisenberg group. In particular, we provide a horizontal version of Minty's theorem concerning maximal H-monotone operators defined in…

We prove new conditional bounds on the the $m$-torsion of class groups of number fields of any fixed degree, for $m=2$, $3$, $4$, and $5$. Our methods first recast the problem in the language of class groups of Galois modules, which allows…

We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that…

Hans Zassenhaus conjectured that every torsion unit of the integral group ring of a finite group $G$ is conjugate within the rational group algebra to an element of the form $\pm g$ with $g\in G$. This conjecture has been disproved recently…

We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.

We bound the higher-order Dehn functions and other filling invariants of certain Carnot groups using approximation techniques. These groups include the higher-dimensional Heisenberg groups, jet groups, and central products of two-step…

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive…

The aim of this work is the study of left-invariant magnetic fields on 2-step nilpotent Lie groups. While the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the…

The main aim of this paper is the description of a large class of lattices in some nilpotent Lie groups, sometimes filiformes, carrying a flat left invariant linear connection anf often a left invariant symplectic form. As a consequence we…