Displaying similar documents to “Some lattice properties of normal-by-finite subgroups”

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 ∈ Hall π ( G ) such that H ∩ V ∈ Hall π ( V ) and 1 ≠ H ∩ U ∈ Hall π ( U ) . Suppose also H ∩ U is a Hall π-sub-group of some S-permutable subgroup of G. Then H ∩ U ∩ V ∈ Hall π ( U ∩ V ) and 〈 H ∩ U , H ∩ V 〉 ∈ Hall π ( 〈 U ∩ 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...

Groups with complete lattice of nearly normal subgroups.

Maria De Falco, Carmela Musella (2002)

Revista Matemática Complutense

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A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given. ...

Groups with Decomposable Set of Quasinormal Subgroups

de Falco, M., de Giovanni, F. (2001)

Serdica Mathematical Journal

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A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

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 any group and let A be an abelian quasinormal subgroup of G . If n is any positive integer, either odd or divisible by 4 , then we prove that the subgroup A n is also quasinormal in G .

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 → X ∩ D , for all X ≤ G , defines a lattice-endomorphism.