Finite \(p\)-groups in which the number of subgroups of possible order is less than or equal to \(p^3\).

DOI10.1007/S11401-010-0590-7zbMath1216.20014OpenAlexW2069608150MaRDI QIDQ606365

Qinhai Zhang, Ying Sun, Hai Peng Qu

Publication date: 17 November 2010

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-010-0590-7

zbMATH Keywords

metacyclic \(p\)-groupsnumbers of subgroupsgroups of order \(p^n\) with cyclic subgroups of index \(p^2\)inner Abelian \(p\)-groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite nilpotent groups, (p)-groups (20D15)

Related Items (8)

Finite \(p\)-groups with few non-major \(k\)-maximal subgroups ⋮ A note on an “Anzahl” theorem of P. Hall ⋮ Finite groups with the set of the number of subgroups of possible order containing exactly two elements. ⋮ On Hua-Tuan's conjecture. II. ⋮ Finite 2-groups whose number of subgroups of each order are at most \(2^4\) ⋮ Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements ⋮ Some unsolvable conjectures in finite \(p\)-groups ⋮ A connection between the number of subgroups and the order of a finite group

Cites Work

• Groups of prime power order. Vol. 1.
• On Hua-Tuan's conjecture.
• Das ``schiefe Produkt in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehören
• On the Number of Subgroups of Given Order in a Finite p-Group of Exponent p
• Endliche Gruppen I
• A Remark on the Class Field Tower^*
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• Unnamed Item

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