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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.

Groups whose all subgroups are ascendant or self-normalizing

63%

Kurdachenko L., Otal J., Russo A., Vincenzi G.

Open Mathematics

2011

tom 9

nr 2

420-432

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, Math. Z., 1972, 125(1), 1–16].

Ograniczanie wyników

2 Open Mathematics

1 Camp-Mora S.

1 Kurdachenko L.

1 Otal J.

1 Russo A.

1 Vincenzi G.

1 2013

1 2011

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Groups with every subgroup ascendant-by-finite

Groups whose all subgroups are ascendant or self-normalizing