Modular embeddings and rigidity for Fuchsian groups

Robert A. Kucharczyk

Displaying similar documents to “Modular embeddings and rigidity for Fuchsian groups”

Modular elements in congruence lattices of $G$ -sets.

Vernikov, Boris M. (2000)

Beiträge zur Algebra und Geometrie

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Subgroups and modular representations of finite quasisimple groups

A. S. Kondratev (1990)

Banach Center Publications

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Groups with metamodular subgroup lattice

M. De Falco, F. de Giovanni, C. Musella, R. Schmidt (2003)

Colloquium Mathematicae

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A group G is called metamodular if for each subgroup H of G either the subgroup lattice 𝔏(H) is modular or H is a modular element of the lattice 𝔏(G). Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.

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.

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...

Normalizers of intermediate congruence subgroups of the Hecke subgroups

Bo-Hae Im, Daeyeol Jeon, Chang Heon Kim (2017)

Open Mathematics

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For a square-free positive integer N, we study the normalizer of ΓΔ(N) in PSL2(ℝ) and investigate the group structure of its quotient by ΓΔ(N) under certain conditions.

Hecke Operators on Congruence Subgroups of the Modular Group

R.A. Rankin (1967)

Mathematische Annalen

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The modular degree and the congruence number of a weight 2 cusp form

Alina Carmen Cojocaru, Ernst Kani (2004)

Acta Arithmetica

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Modular Frobenius Groups.

E.B. Kuisch, Robert W. van der Waall (1996)

Manuscripta mathematica

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On Goldie absolute direct summands in modular lattices

Rupal Shroff (2023)

Mathematica Bohemica

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Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands....