Displaying similar documents to “Isotype knice subgroups of global Warfield groups”

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...

On some soluble groups in which U -subgroups form a lattice

Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)

Commentationes Mathematicae Universitatis Carolinae

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The article is dedicated to groups in which the set of abnormal and normal subgroups ( U -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.

On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

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New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.