Displaying similar documents to “Frattini normal subgroups of finite groups.”

On E-S-supplemented subgroups of finite groups

Changwen Li, Xuemei Zhang, Xiaolan Yi (2013)

Colloquium Mathematicae

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The major aim of the present paper is to strengthen a nice result of Shemetkov and Skiba which gives some conditions under which every non-Frattini G-chief factor of a normal subgroup E of a finite group G is cyclic. As applications, some recent known results are generalized and unified.

Conditions for p-supersolubility and p-nilpotency of finite soluble groups

Wenai Yan, Baojun Li, Zhirang Zhang (2013)

Colloquium Mathematicae

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Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.

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 supplements of subgroups of finite groups

Xianhua Li, A. Ballester-Bolinches (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.

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...