Finite \(p\)-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order \(p^3\)

DOI10.1007/S10114-019-7308-XOpenAlexW2946480263WikidataQ127876830 ScholiaQ127876830MaRDI QIDQ2311737

Qinhai Zhang

Publication date: 4 July 2019

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-019-7308-x

zbMATH Keywords

finite \(p\)-groups\(p\)-groups of maximal classa minimal nonabelian subgroupthe Hughes subgroup

Mathematics Subject Classification ID

Special subgroups (Frattini, Fitting, etc.) (20D25) Finite nilpotent groups, (p)-groups (20D15)

Related Items (3)

At-groups with t + 1 generators ⋮ ISOLATED SUBGROUPS OF FINITE p-GROUPS ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Finite \(p\)-groups with exactly one \(\mathcal A_1\)-subgroup of given structure of order \(p^3\).
• Finite metahamiltonian \(p\)-groups.
• Finite \(p\)-groups with a class of complemented normal subgroups
• Finite \(p\)-groups all of whose non-Abelian proper subgroups are generated by two elements.
• Groups of prime power order. Vol. 1.
• Groups of prime power order. Vol. 2.
• Finite \(p\)-groups with a minimal non-Abelian subgroup of index \(p\). I.
• Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). II.
• Finite \(p\)-groups all of whose subgroups of index \(p^3\) are Abelian.
• On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4.
• Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). III.
• 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
• Finite p-groups with a minimal non-abelian subgroup of index p (V)
• The intersection of nonabelian subgroups of finite p-groups
• Finite p-Groups All of Whose Subgroups of Index p² Are Abelian
• Intersection of maximal subgroups which are not minimal nonabelian of finite p-groups
• $\mathcal{A}_t$-GROUPS SATISFYING A CHAIN CONDITION
• Finite p-groups with a minimal non-abelian subgroup of index p (IV)
• On the H p -Problem for Finite p-Groups

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