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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.

Strongly bounded automorphism groups

A. Ivanov (2006)

Colloquium Mathematicae

A group G is strongly bounded if every isometric action of G on a metric space has bounded orbits. We show that the automorphism groups of typical countable structures with the small index property are strongly bounded. In particular we show that this is the case when G is the automorphism group of the countable universal locally finite extension of a periodic abelian group.

Sulle S-partizioni strette nei gruppi localmente finiti

Guido Zappa (1985)

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

A characterization of strict S-partitions in locally finite groups is given.

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