Search results for "UPS"

Near abelian profinite groups

2012

Abstract A compact p-group G (p prime) is called near abelian if it contains an abelian normal subgroup A such that G/A has a dense cyclic subgroup and that every closed subgroup of A is normal in G. We relate near abelian groups to a class of compact groups, which are rich in permuting subgroups. A compact group is called quasihamiltonian (or modular) if every pair of compact subgroups commutes setwise. We show that for p ≠ 2 a compact p-group G is near abelian if and only if it is quasihamiltonian. The case p = 2 is discussed separately.

Representations of Finite Groups

2009

Uncountable existentially closed groups in locally finite group classes

1990

In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only per…

Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher

2016

International audience

Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

2018

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty $$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

Locally compact groups which are just not compact

2010

A Just-Non-Compact group, or briefly a JNC group, is a Hausdorff topological group which is not a compact group but all of whose proper Hausdorff quotients are compact groups. Intuitively, it is clear that these groups are rich in compact quotients. Locally compact JNC groups are largely described in the present paper.

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

2017

AbstractCarnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

Solutions and positive solutions for superlinear Robin problems

2019

We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.

A multiplicity theorem for parametric superlinear (p,q)-equations

2020

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Lévy flights and Lévy-Schrödinger semigroups

2010

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.