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

Patrizia Longobardi; Mercede Maj

The search session has expired. Please query the service again.

Displaying similar documents to “Some remarks on groups in which elements with the same $p$ -power commute”

Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup

Anna Luisa Gilotti (1990)

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

Similarity:

In this paper it is proved that a finite group G with an automorphism $α$ of prime order r, such that $C_{G} (α) = 1$ is contained in a nilpotent subgroup H, with $(|H|, r) = 1$ , is nilpotent provided that either $|H|$ is odd or, if $|H|$ is even, then r is not a Fermât prime.

On almost finitely generated nilpotent groups.

Hilton, Peter, Militello, Robert (1996)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Some remarks on almost finitely generated nilpotent groups.

Peter Hilton, Robert Militello (1992)

Publicacions Matemàtiques

Similarity:

We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if G_p is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that G_p ≅ H_p for all p. The we have proper set-inclusions: {fg} ⊂ {fg-like} ⊂ {fgp}. We examine the extent to which fg-like nilpotent groups satisfy the axioms for...

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....

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 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

Similarity:

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 $k$ .

Displaying similar documents to “Some remarks on groups in which elements with the same p -power commute”

Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup

On almost finitely generated nilpotent groups.

Some remarks on almost finitely generated nilpotent groups.

On absolutely-nilpotent of class k groups

On locally finite groups and the centralizers of automorphisms

A nilpotency condition for finitely generated soluble groups

Displaying similar documents to “Some remarks on groups in which elements with the same $p$ -power commute”

On absolutely-nilpotent of class $k$ groups