On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

L. A. Kurdachenko; I. Ya. Subbotin; T. I. Ermolkevich

Displaying similar documents to “On non-periodic groups whose finitely generated subgroups are either permutable or pronormal”

Artinian and noetherian factorized groups

Bernhard Amberg (1976)

Rendiconti del Seminario Matematico della Università di Padova

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Groups whose all subgroups are ascendant or self-normalizing

Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)

Open Mathematics

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This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups,...

On non-supersoluble and non-polycyclic normal subgroups

James C. Beidleman, Howard Smith (1993)

Rendiconti del Seminario Matematico della Università di Padova

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On the structure of groups whose non-abelian subgroups are subnormal

Leonid Kurdachenko, Sevgi Atlıhan, Nikolaj Semko (2014)

Open Mathematics

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The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.

Soluble products of two locally finite groups with min- $p$ for every prime $p$

Bernhard Amberg (1983)

Rendiconti del Seminario Matematico della Università di Padova

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Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

Open Mathematics

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We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at...

Groups with every subgroup ascendant-by-finite

Sergio Camp-Mora (2013)

Open Mathematics

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A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

Groups with many nearly normal subgroups

Maria De Falco (2001)

Bollettino dell'Unione Matematica Italiana

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Un sottogruppo $H$ di un gruppo $G$ si dice nearly normal se ha indice finito nella sua chiusura normale $H^{G}$ . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria $χ$ per diverse scelte naturali della proprietà $χ$ .