On the Intersection of the Normalizers of the Nilpotent Residuals of All Subgroups of a Finite Group

DOI10.1142/S1005386713000321zbMath1281.20020OpenAlexW2007678683MaRDI QIDQ4923909

Lü Gong, Xiu Yun Guo

Publication date: 27 May 2013

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

Full work available at URL: https://doi.org/10.1142/s1005386713000321

zbMATH Keywords

finite groupsnilpotent residualsascending seriesintersections of normalizersgeneralized norm

Mathematics Subject Classification ID

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

Related Items (10)

A note on Itô’s theorem of p-nilpotence ⋮ 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 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. ⋮ Unnamed Item ⋮ 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 Generalized Norms of Finite Groups ⋮ On the generalized norms of finite groups

Cites Work

• Über den Normalisator der subnormalen Untergruppen
• On the intersection of the normalizers of derived subgroups of all subgroups of a finite group.
• The Wielandt length of finite groups
• The Wielandt Subgroup of a Finite Soluble Group
• On minimal subgroups of finite groups
• Centre and norm

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