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Some remarks on almost finitely generated nilpotent groups.

Peter Hilton, Robert Militello (1992)

Publicacions Matemàtiques

We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp 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 a Serre class. We obtain a complete answer only in the case that [G, G] is finite. (The collection of fgp nilpotent 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

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.

Some remarks on simple Bol loops

Gábor P. Nagy (2008)

Commentationes Mathematicae Universitatis Carolinae

In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.

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