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Displaying similar documents to “Conditions for p-supersolubility and p-nilpotency of finite soluble groups”

Pronormal and subnormal subgroups and permutability

James Beidleman, Hermann Heineken (2003)

Bollettino dell'Unione Matematica Italiana

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We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow p -subgroups for p < 7 permute with all subnormal 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...

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.

OnCSQ-normal subgroups of finite groups

Yong Xu, Xianhua Li (2016)

Open Mathematics

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We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.