Pronormal and subnormal subgroups and permutability

James Beidleman; Hermann Heineken

Displaying similar documents to “Pronormal and subnormal subgroups and permutability”

A contribution to the theory of finite supersoluble groups

Luis M. Ezquerro (1993)

Rendiconti del Seminario Matematico della Università di Padova

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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...

Finite groups with few conjugacy classes of subgroups

Rolf Brandl, Libero Verardi (1992)

Rendiconti del Seminario Matematico della Università di Padova

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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.

Maximal subgroups and PST-groups

Adolfo Ballester-Bolinches, James Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig (2013)

Open Mathematics

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A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable...

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.