On the norm of the nilpotent residuals of all subgroups of a finite group.

DOI10.1016/J.JALGEBRA.2011.11.018zbMath1255.20019OpenAlexW2027135860MaRDI QIDQ435944

Guohua Qian, Zhencai Shen, Wujie Shi

Publication date: 13 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.11.018

zbMATH Keywords

finite groupsFitting lengthsnilpotent residualsintersections of normalizersmetanilpotent groups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Series and lattices of subgroups (20D30) Finite nilpotent groups, (p)-groups (20D15)

Related Items (19)

On the \(\sigma \)-nilpotent norm and the \(\sigma \)-nilpotent hypernorm of a finite group ⋮ On normalizers of the nilpotent residuals of subgroups of a finite group ⋮ On the nilpotent residual norm of a group and the structure of \(S\)-groups ⋮ On the normalizers of p-nilpotency-residuals of all subgroups in a finite group ⋮ On the \(\pi\mathfrak F\)-norm and the \(\mathfrak H\)-\(\mathfrak F\)-norm of a finite group. ⋮ On PN-groups and the norm of minimal subgroups ⋮ On the normalizers of \(\mathcal F\)-residuals of all subgroups of a finite group. ⋮ Unnamed Item ⋮ ON THEσ-NILPOTENT NORM AND THEσ-NILPOTENT LENGTH OF A FINITE GROUP ⋮ The norm of p-decomposable residuals of all subgroups in a finite group ⋮ On the generalized norms of a group ⋮ ON THE $\mathcal {F}$-RESIDUALS NORM OF A GROUP ⋮ On the intersection of the normalizers of the \(\mathcal F\)-residuals of subgroups of a finite group. ⋮ On the generalized norm of a finite group ⋮ On the \(\mathcal{F}^*\)-norm of a finite group ⋮ On Generalized Norms of Finite Groups ⋮ On the \(\mathfrak{F} \)-norm of a finite group ⋮ Derived norms of finite groups ⋮ On the Nσ*-norm and Dp*-norm of finite groups

Cites Work

• A note on intersections of maximal \(\mathcal F\)-subgroups.
• Classes of finite groups and their properties
• Über den Normalisator der subnormalen Untergruppen
• Some sufficient conditions for a group to be nilpotent
• On the norm of a group
• Finite groups with its power automorphism groups having small indices.
• On the intersection of the normalizers of derived subgroups of all subgroups of a finite group.
• A property of the lower central series of a group
• The Wielandt length of finite groups
• Finite groups whose minimal subgroups are normal
• The Wielandt Subgroup of a Finite Soluble Group
• Centre and norm
• Endliche Gruppen I
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