Displaying similar documents to “Finite groups with modular chains”

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.

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 ).

On modular projective representations of finite nilpotent groups

Leonid F. Barannyk, Kamila Sobolewska (2001)

Colloquium Mathematicae

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Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.

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...

Some remarks on almost finitely generated nilpotent groups.

Peter Hilton, Robert Militello (1992)

Publicacions Matemàtiques

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We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp for all p. The we have proper set-inclusions: {fg} ⊂ {fg-like} ⊂ {fgp}. We examine the extent to which fg-like nilpotent groups satisfy the axioms for...