Equivalent conditions for p-nilpotence

Keresztély Corrádi; Erzsébet Horváth

Displaying similar documents to “Equivalent conditions for p-nilpotence”

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

Similarity:

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

Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host, Bryna Kra (2008)

Bulletin de la Société Mathématique de France

Similarity:

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.

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

Similarity:

A group $G$ in a variety $V$ is said to be absolutely- $V$ , and we write $G \in A V$ , 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....

Remarks on Characters of Discrete Nilpotent Groups.

Ernest Plonka (1979)

Mathematische Annalen

Similarity:

On locally finite groups and the centralizers of automorphisms

Pavel Shumyatsky (2001)

Bollettino dell'Unione Matematica Italiana

Similarity:

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 $[C_{G} (a), \underset{m}{\underset{︸}{C_{G} (b), \dots, C_{G} (b)}}] = 1$ per ogni $a, b \in A^{♯}$ . In questo articolo si dimostra che $G$ è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da $p$ e $m$ .

A note on the converse of the Clifford's theorem and some consequences

G. Navarro (1987)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

$G$ -тождества нильпотентных групп. I

М.Г. Амаглобели (2001)

Algebra i Logika

Similarity:

Hurewicz-Serre theorem in extension theory

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

Fundamenta Mathematicae

Similarity:

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 ∈...

A remark on a Theorem of J. G. Thompson

Bertram Huppert (1998)

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

Similarity:

An important theorem by J. G. Thompson says that a finite group $G$ is $p$ -nilpotent if the prime $p$ divides all degrees (larger than 1) of irreducible characters of $G$ . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary $p$ -lenght, in which the lenght of any conjugacy class of non central elements is divisible by $p$ .