Subgroups of locally normal groups

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.

Inert subgroups of uncountable locally finite groups

Barbara Majcher-Iwanow (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be an uncountable universal locally finite group. We study subgroups $H < G$ such that for every $g \in G$ , $| H : H \cap H^{g} | < | H |$ .

On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

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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 some soluble groups in which $U$ -subgroups form a lattice

Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)

Commentationes Mathematicae Universitatis Carolinae

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The article is dedicated to groups in which the set of abnormal and normal subgroups ( $U$ -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.

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