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Groups with every subgroup ascendant-by-finite

100%

Camp-Mora S.

Open Mathematics

2013

tom 11

nr 12

2182-2185

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.

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

100%

Kurdachenko L., Atlıhan S., Semko N.

Open Mathematics

2014

tom 12

nr 12

1762-1771

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.

Ograniczanie wyników

2 Open Mathematics

1 Atlıhan S.

1 Camp-Mora S.

1 Kurdachenko L.

1 Semko N.

1 2014

1 2013

Wyniki wyszukiwania

Groups with every subgroup ascendant-by-finite

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