Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). III.

DOI10.1007/s11425-014-4892-1zbMath1330.20029arXiv1310.5496OpenAlexW1971653719MaRDI QIDQ2515306

Lijian An, Ming-Yao Xu, Hai Peng Qu

Publication date: 31 July 2015

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5496

zbMATH Keywords

maximal subgroupsfinite \(p\)-groupsregular \(p\)-groups\(p\)-groups of maximal classmetahamiltonian groupsmetabelian \(p\)-groupsminimal non-Abelian \(p\)-groups\(\mathcal A_t\)-groupssubgroups of index \(p\)

Mathematics Subject Classification ID

Finite nilpotent groups, (p)-groups (20D15)

Related Items (10)

Finite \(p\)-groups whose nonnormal subgroups are metacyclic ⋮ 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 \(\leq p\). ⋮ Finitep-Groups All of Whose Minimal Nonnormal Subgroups Posses Large Normal Closures ⋮ 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 \(p^3\) ⋮ Finite \(p\)-groups whose length of chain of nonnormal subgroups is at most 2 ⋮ Finite \(p\)-groups all of whose subgroups of index \(p^3\) are Abelian.

Cites Work

• Unnamed Item
• Finite metahamiltonian \(p\)-groups.
• Groups of prime power order. Vol. 1.
• Finite \(p\)-groups with a minimal non-Abelian subgroup of index \(p\). I.
• A classification of finite metahamiltonian \(p\)-groups
• 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.
• Finite p-groups with a minimal non-abelian subgroup of index p (V)
• The Groups of Order p 6 (p and Odd Prime)
• Finite p-groups with a minimal non-abelian subgroup of index p (IV)

This page was built for publication: Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). III.