Groups with nearly modular subgroup lattice

Francesco de Giovanni; Carmela Musella

Displaying similar documents to “Groups with nearly modular subgroup lattice”

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.

Dual-Dedekind subgroups in finite groups

Federico Menegazzo (1971)

Rendiconti del Seminario Matematico della Università di Padova

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Normal subgroups and projectivities of finite groups

Federico Menegazzo (1978)

Rendiconti del Seminario Matematico della Università di Padova

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On lattice properties of S-permutably embedded subgroups of finite soluble groups

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

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In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H \in {Hall}_{π} (G)$ such that $H \cap V \in {Hall}_{π} (V)$ and $1 \neq H \cap U \in {Hall}_{π} (U)$ . Suppose also $H \cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H \cap U \cap V \in {Hall}_{π} (U \cap V)$ and $〈 H \cap U, H \cap V 〉 \in {Hall}_{π} (〈 U \cap V 〉)$ . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders...

Some lattice properties of normal-by-finite subgroups

Maria De Falco, Carmela Musella (2003)

Bollettino dell'Unione Matematica Italiana

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A subgroup $H$ of a group $G$ is said to be normal-by-finite if the core $H_{G}$ of $H$ in $G$ has finite index in $H$ . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then $G$ is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set $nf (G)$ consisting of all normal-by-finite subgroups satisfies certain...

On the number of subgroups of given index in the modular group.

W. Imrich, R. Razen (1979)

Monatshefte für Mathematik

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Direct products with isomorphic lattices

Charles S. Holmes (1971)

Rendiconti del Seminario Matematico della Università di Padova

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Dual-standard subgroups in nonperiodic locally soluble groups

Stewart E. Stonehewer, Giovanni Zacher (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map $X \to X \cap D$ , for all $X \leq G$ , defines a lattice-endomorphism.