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A note on groups with few isomorphism classes of subgroups

100%

de Giovanni F., Russo A.

Colloquium Mathematicum

2016

tom 144

nr 2

265-271

The structure of infinite groups in which any two (proper) subgroups of the same cardinality are isomorphic is described within the universe of locally graded groups. The corresponding problem for finite groups was considered by R. Armstrong (1958).

Groups whose all subgroups are ascendant or self-normalizing

81%

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

1 Colloquium Mathematicum

1 Open Mathematics

2 Russo A.

1 Kurdachenko L.

1 Otal J.

1 Vincenzi G.

1 de Giovanni F.

1 2016

1 2011

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A note on groups with few isomorphism classes of subgroups

Groups whose all subgroups are ascendant or self-normalizing