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On locally finite minimal non-solvable groups

Ahmet Arıkan, Sezgin Sezer, Howard Smith (2010)

Open Mathematics

In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.

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

L. A. Kurdachenko, I. Ya. Subbotin, T. I. Ermolkevich (2013)

Mathematica Bohemica

The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let G be a locally generalized radical...

On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.

On the derived length of parasoluble groups

Alessio Russo (2003)

Bollettino dell'Unione Matematica Italiana

In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.

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