Displaying similar documents to “Fixed points of discrete nilpotent group actions on S 2 ”

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.

A nilpotency condition for finitely generated soluble groups

Costantino Delizia (1998)

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

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We prove that if k > 1 is an integer and G is a finitely generated soluble group such that every infinite set of elements of G contains a pair which generates a nilpotent subgroup of class at most k , then G is an extension of a finite group by a torsion-free k -Engel group. As a corollary, there exists an integer n , depending only on k and the derived length of G , such that G / Z n ⁢ G is finite. For k < 4 , such n depends only on k .

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 .

Some remarks on groups in which elements with the same p -power commute

Patrizia Longobardi, Mercede Maj (1999)

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

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In this paper we characterize certain classes of groups G in which, from x p = y p ( x , y ∈ G , p a fixed prime), it follows that x ⁢ y = y ⁢ x . Our results extend results previously obtained by other authors, in the finite case.

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...

Infinite locally soluble k -Engel groups

Lucia Serena Spiezia (1992)

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

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In this paper we deal with the class E k * of groups G for which whenever we choose two infinite subsets X , Y there exist two elements x ∈ X , y ∈ Y such that x , y , … , y ︸ k = 1 . We prove that an infinite finitely generated soluble group in the class E k * is in the class E k of k -Engel groups. Furthermore, with k = 2 , we show that if G ∈ E 2 * is infinite locally soluble or hyperabelian group then G ∈ E 2 .