Some characterizations of finite \(\sigma\)-soluble \(P\sigma T\)-groups

DOI10.1016/j.jalgebra.2017.11.009zbMath1378.20027arXiv1704.02509OpenAlexW2767381779MaRDI QIDQ1682069

Alexander N. Skiba

Publication date: 28 November 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.02509

zbMATH Keywords

finite group\(\sigma\)-nilpotent group\(\sigma\)-permutable subgroup\(\sigma\)-soluble group\(P\sigma T\)-group

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Series and lattices of subgroups (20D30) Finite nilpotent groups, (p)-groups (20D15) Products of subgroups of abstract finite groups (20D40)

Related Items

Separated lattices of multiply \(\sigma \)-local formations ⋮ Characterizations of \(\sigma \)-solvable finite groups ⋮ On the \(\sigma \)-nilpotent norm and the \(\sigma \)-nilpotent hypernorm of a finite group ⋮ Finite groups with generalized subnormal and generalized permutable subgroups ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On \(\Pi \)-permutable subgroups in finite groups ⋮ Unnamed Item ⋮ On \(\sigma\)-supersoluble groups and one generalization of \textit{CLT}-groups ⋮ Laws of the lattices of \(\sigma \)-local formations of finite groups ⋮ A generalization of \(\sigma\)-permutability ⋮ Unnamed Item ⋮ On finite Sylow tower and σ-tower groups ⋮ On σ-inductive lattices of n-multiply σ-local formations of finite groups ⋮ On the distributivity and modularity signs of a family of fitting sets of a finite group ⋮ Finite groups with \(\sigma \)-abnormal Schmidt subgroups ⋮ On Lockett's conjecture for \(\sigma \)-local Fitting classes ⋮ On properties of the lattice of all τ -closed n -multiply σ -local formations ⋮ A Robinson description of finite \(P\sigma T\)-groups ⋮ Characterizations of some classes of finite σ -soluble PσT -groups ⋮ New characterizations of \(\sigma\)-nilpotent finite groups ⋮ A characterization of finite \(\sigma\)-soluble \(P \sigma T\)-groups ⋮ ON -QUASINORMAL SUBGROUPS OF FINITE GROUPS ⋮ On Baer-σ-local formations of finite groups ⋮ Unnamed Item ⋮ Onm-S-supplemented subgroups of finite groups ⋮ A new characterization of finite \(\sigma \)-soluble \(P\sigma T \)-groups ⋮ Finite groups with weakly subnormal and partially subnormal subgroups ⋮ ON THEσ-NILPOTENT NORM AND THEσ-NILPOTENT LENGTH OF A FINITE GROUP ⋮ Unnamed Item ⋮ A criterion for a finite group to be σ-soluble ⋮ On dualization of a result of Bryce and Cossey theory ⋮ A GENERALISATION OF FINITEPT-GROUPS ⋮ Finite groups with given weakly $\tau_{\sigma}$-quasinormal subgroups ⋮ On strongly \(\Pi \)-permutable subgroups of a finite group ⋮ On weakly m-σ-permutable subgroups of finite groups ⋮ On n-multiply σ-local formations of finite groups ⋮ On generalized m-S-permutable subgroups of a finite group ⋮ Finite generalized soluble groups ⋮ Characterizations of finite \(\sigma\)-nilpotent and \(\sigma\)-quasinilpotent groups ⋮ Subnormality and residuals for saturated formations: a generalization of Schenkman's theorem ⋮ Finite groups with σ-Frobenius condition for non-normal σ-primary subgroups ⋮ \(G\)-covering subgroup systems for some classes of \(\sigma\)-soluble groups ⋮ Finite groups with \(\sigma\)-subnormal Schmidt subgroups ⋮ On sublattices of the subgroup lattice defined by formation Fitting sets ⋮ Criteria for \(\sigma \)-solvability and meta-\( \sigma \)-nilpotency of a finite group ⋮ On the lattice of all \(\mathcal{H} \)-permutable subgroups of a finite group ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the distributivity and modularity properties of the lattice of Fitting classes ⋮ Unnamed Item ⋮ On the generalized \(\sigma\)-Fitting subgroup of finite groups ⋮ On semi-σ-nilpotent finite groups ⋮ Finite groups with weakly m-σ-permutable subgroups ⋮ On \({\Sigma}_t^{\sigma }\)-closed classes of finite groups ⋮ On \(\sigma\)-embedded and \(\sigma\)-\(n\)-embedded subgroups of finite groups ⋮ On \(\sigma\)-local Fitting classes ⋮ On the \(\sigma \)-nilpotent hypercenter of finite groups ⋮ Finite groups with K--subnormal Schmidt subgroups ⋮ Some properties of n-multiply σ-local formations of finite groups ⋮ On weakly σ-semipermutable subgroups of finite groups

Cites Work

• Unnamed Item
• Some new characterizations of PST-groups.
• On the \(\pi'\)-properties of a finite group possessing a Hall \(\pi\)-subgroup.
• Products of finite groups.
• Subnormal, permutable, and embedded subgroups in finite groups.
• Finite groups in which normality or quasinormality is transitive.
• Finite soluble groups
• Groups in which Sylow subgroups and subnormal subgroups permute.
• Subgroup lattices of finite groups which properly contain the lattice of subnormal subgroups
• Sylow permutable subnormal subgroups of finite groups
• Finite groups with permutable complete Wielandt sets of subgroups.
• On \(\sigma\)-subnormal and \(\sigma\)-permutable subgroups of finite groups.
• On some results in the theory of finite partially soluble groups
• Totally permutable products of finite groups satisfying SC or PST.
• The structure of finite groups in which permutability is a transitive relation
• Structure Theory for Canonical Classes of Finite Groups
• Finite Groups whose Subnormal Subgroups Permute with all Sylow Subgroups
• A Local Approach to Certain Classes of Finite Groups
• Some characterizations of finite groups in which semipermutability is a transitive relation
• Classes of Finite Groups
• Endliche Gruppen I
• Finite soluble groups with permutable subnormal subgroups