Subgroups and normal subgroups as systems of ideals

František Voráč

Normal subgroups as ideals

Bohumil Šmarda, Markku Niemenmaa (1983)

Archivum Mathematicum

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Some group theoretic problems inspired by ring theoretic analogies.

Pálfy, Péter P., Steinfeld, Ottó (2002)

Mathematica Pannonica

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$K$ -essential subgroups of abelian groups. III.

Jindřich Bečvář (1977)

Commentationes Mathematicae Universitatis Carolinae

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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...

Displaying similar documents to “Subgroups and normal subgroups as systems of ideals”

Normal subgroups as ideals

Some group theoretic problems inspired by ring theoretic analogies.

K -essential subgroups of abelian groups. III.

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

$K$ -essential subgroups of abelian groups. III.