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## Colloquium Mathematicum

2001 | 88 | 1 | 13-20
Tytuł artykułu

### Groups with nearly modular subgroup lattice

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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.
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13-20
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wydano
2001
Twórcy
• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
autor
• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
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