Displaying similar documents to “Groups with metamodular subgroup lattice”

Groups with nearly modular subgroup lattice

Francesco de Giovanni, Carmela Musella (2001)

Colloquium Mathematicae

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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...

Finite groups with modular chains

Roland Schmidt (2013)

Colloquium Mathematicae

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In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.

Strongly modular lattices with long shadow

Gabriele Nebe (2004)

Journal de Théorie des Nombres de Bordeaux

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This article classifies the strongly modular lattices with longest and second longest possible shadow.

Modular embeddings and rigidity for Fuchsian groups

Robert A. Kucharczyk (2015)

Acta Arithmetica

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We prove a rigidity theorem for semiarithmetic Fuchsian groups: If Γ₁, Γ₂ are two semiarithmetic lattices in PSL(2,ℝ ) virtually admitting modular embeddings, and f: Γ₁ → Γ₂ is a group isomorphism that respects the notion of congruence subgroups, then f is induced by an inner automorphism of PGL(2,ℝ ).