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Groups with nearly modular subgroup lattice

100%

de Giovanni F., Musella C.

Colloquium Mathematicum

2001

tom 88

nr 1

13-20

A subgroup H of a group G is nearly normal if it has finite index in its normal closure $H^{G}$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we study the structure of groups in which all subgroups are nearly modular, proving in particular that a locally graded group with this property has locally finite commutator subgroup.

Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

81%

De Falco M., de Giovanni F., Musella C.

Colloquium Mathematicum

2013

tom 131

nr 2

233-239

It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Musella C.

2 de Giovanni F.

1 De Falco M.

1 2013

1 2001

Wyniki wyszukiwania

Groups with nearly modular subgroup lattice

Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank