Displaying similar documents to “Groups whose proper subgroups are locally finite-by-nilpotent”

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 .

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 .

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....

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.

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.