Finite p-groups with a minimal non-abelian subgroup of index p (IV)

DOI10.1142/S0219498815500206zbMath1317.20018arXiv1310.5503OpenAlexW3166323200MaRDI QIDQ5498576

Ruifang Hu, Lijian An, Qinhai Zhang

Publication date: 9 February 2015

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5503

zbMATH Keywords

maximal subgroupsfinite \(p\)-groupsgenerators and relationsminimal non-Abelian \(p\)-groups\(\mathcal A_t\)-groupssubgroups of index \(p\)

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (13)

Finite 𝒟C-groups ⋮ On edge-transitive metacyclic covers of cubic arc-transitive graphs of order twice a prime ⋮ Finite \(p\)-groups whose nonnormal subgroups are metacyclic ⋮ Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal ⋮ 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 maximal subgroups either are metacyclic or have a derived subgroup of order \(\leq p\). ⋮ Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). III. ⋮ A classification of finite metahamiltonian \(p\)-groups ⋮ Intersection of maximal subgroups which are not minimal nonabelian of finite p-groups ⋮ Finite \(p\)-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order \(p^3\) ⋮ The number of conjugacy classes of nonnormal subgroups of finite p-groups (III) ⋮ Finite \(p\)-groups all of whose subgroups of index \(p^3\) are Abelian.

Cites Work

• Finite \(p\)-groups all of whose non-Abelian proper subgroups are generated by two elements.
• Groups of prime power order. Vol. 1.
• 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 with few minimal nonabelian subgroups.
• 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)
• On the structure of the automorphism group of a minimal nonabelian p-group (metacyclic case)

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