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...

The 4-string braid group B 4 has property RD and exponential mesoscopic rank

Sylvain Barré, Mikaël Pichot (2011)

Bulletin de la Société Mathématique de France

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We prove that the braid group B 4 on 4 strings, its central quotient B 4 / 〈 z 〉 , and the automorphism group Aut ( F 2 ) of the free group F 2 on 2 generators, have the property RD of Haagerup–Jolissaint. We also prove that the braid group B 4 is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.