Displaying similar documents to “On groups of automorphisms of nilpotent p -groups of finite rank”

Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host, Bryna Kra (2008)

Bulletin de la Société Mathématique de France

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In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions 2 and 3 and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

Hurewicz-Serre theorem in extension theory

M. Cencelj, J. Dydak, A. Mitra, A. Vavpetič (2008)

Fundamenta Mathematicae

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The paper is devoted to generalizations of the Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to their homology groups. Here are the main results of the paper: Theorem 0.1. Let L be a nilpotent CW complex and F the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that X τ K ( H k ( L ) , k ) for all k ≥ 1, then X τ K ( π k ( F ) , k ) and X τ K ( π k ( L ) , k ) for all k ≥ . Theorem 0.2. Let X be a metrizable space such that dim(X) < ∞ or X ∈...

Convergence of formal solutions of first order singular partial differential equations of nilpotent type

Masatake Miyake, Akira Shirai (2012)

Banach Center Publications

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Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: P u ( x , y , z ) : = ( y ∂ x - z ∂ y ) u ( x , y , z ) = f ( x , y , z ) ∈ x , y , z , where P = y ∂ x - z ∂ y : x , y , z → x , y , z . For this equation, our aim is to characterize the solvability on x , y , z by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.

On absolutely-nilpotent of class k groups

Patrizia Longobardi, Trueman MacHenry, Mercede Maj, James Wiegold (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A group G in a variety V is said to be absolutely- V , and we write G ∈ A ⁢ V , if central extensions by G are again in V . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class A ⁢ N k of absolutely-nilpotent of class k groups. We prove some closure properties of the class A ⁢ N k and we show that every nilpotent of class k group can be embedded in an A ⁢ N k -gvoup. We describe all metacyclic A ⁢ N k -groups and we characterize 2 -generator and infinite 3 -generator A ⁢ N 2 -groups....

On nilpotent operators

Laura Burlando (2005)

Studia Mathematica

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We give several necessary and sufficient conditions in order that a bounded linear operator on a Banach space be nilpotent. We also discuss three necessary conditions for nilpotency. Furthermore, we construct an infinite family (in one-to-one correspondence with the square-summable sequences ( ε ₙ ) n ∈ ℕ of strictly positive real numbers) of nonnilpotent quasinilpotent operators on an infinite-dimensional Hilbert space, all the iterates of each of which have closed range. Each of these operators...

Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center

Bin Ren, Lin Sheng Zhu (2017)

Czechoslovak Mathematical Journal

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A Lie algebra L is called 2-step nilpotent if L is not abelian and [ L , L ] lies in the center of L . 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center.

On locally finite groups and the centralizers of automorphisms

Pavel Shumyatsky (2001)

Bollettino dell'Unione Matematica Italiana

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Sia p un primo, e A un gruppo abeliano elementare di ordine p 2 che agisce sul p ′ -gruppo localmente finito G . Supponiamo che esista un intero positivo m tale che C G ⁢ a , C G ⁢ b , … , C G ⁢ b ︸ m = 1 per ogni a , b ∈ A ♯ . In questo articolo si dimostra che G è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da p e m .

Images of locally nilpotent derivations of bivariate polynomial algebras over a domain

Xiaosong Sun, Beini Wang (2024)

Czechoslovak Mathematical Journal

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We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let R be a domain containing a field of characteristic zero. We prove that, when R is a one-dimensional unique factorization domain, the image of any locally nilpotent R -derivation of the bivariate polynomial algebra R [ x , y ] is a Mathieu-Zhao subspace. Moreover, we prove that, when R is a Dedekind domain, the image of a locally nilpotent R -derivation of R [ x , y ] with some...

L p spectral multipliers on the free group N 3 , 2

Alessio Martini, Detlef Müller (2013)

Studia Mathematica

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Let L be a homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent Lie group N 3 , 2 on three generators. We prove a theorem of Mikhlin-Hörmander type for the functional calculus of L, where the order of differentiability s > 6/2 is required on the multiplier.

Partial differential equations in Banach spaces involving nilpotent linear operators

Antonia Chinnì, Paolo Cubiotti (1996)

Annales Polonici Mathematici

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Let E be a Banach space. We consider a Cauchy problem of the type ⎧ D t k u + ∑ j = 0 k - 1 ∑ | α | ≤ m A j , α ( D t j D x α u ) = f in ℝ n + 1 , ⎨ ⎩ D t j u ( 0 , x ) = φ j ( x ) in ℝ n , j=0,...,k-1, where each A j , α is a given continuous linear operator from E into itself. We prove that if the operators A j , α are nilpotent and pairwise commuting, then the problem is well-posed in the space of all functions u ∈ C ∞ ( ℝ n + 1 , E ) whose derivatives are equi-bounded on each bounded subset of ℝ n + 1 .

Sub-Laplacian with drift in nilpotent Lie groups

Camillo Melzi (2003)

Colloquium Mathematicae

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We consider the heat kernel ϕ t corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for ϕ t . We also obtain a large time lower Gaussian estimate for ϕ t .

Leibniz's rule on two-step nilpotent Lie groups

Krystian Bekała (2016)

Colloquium Mathematicae

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Let be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows us to define a generalized multiplication f g = ( f ∨ ∗ g ∨ ) ∧ of two functions in the Schwartz class (*), where ∨ and ∧ are the Abelian Fourier transforms on the Lie algebra and on the dual * and ∗ is the convolution on the group . In the operator analysis on nilpotent Lie groups an important notion is the one of symbolic calculus which can be viewed as a higher order...