Finite \(p\)-groups with a minimal non-Abelian subgroup of index \(p\). I.

DOI10.1016/j.jalgebra.2012.03.007zbMath1262.20023OpenAlexW2046306908MaRDI QIDQ1758538

Hai Peng Qu, Lijian An, Sushan Yang, Ming-Yao Xu

Publication date: 9 November 2012

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2012.03.007

zbMATH Keywords

finite \(p\)-groupsregular \(p\)-groups\(p\)-groups of maximal classmetabelian \(p\)-groupsminimal non-Abelian \(p\)-groups

Mathematics Subject Classification ID

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

Related Items (12)

ISOLATED SUBGROUPS OF FINITE p-GROUPS ⋮ On the finite $p$-groups with unique cyclic subgroup of given order ⋮ 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 \(p\). II. ⋮ Large odd prime power order automorphism groups of algebraic curves in any characteristic ⋮ 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 \(p^3\) ⋮ Finite p-groups with a minimal non-abelian subgroup of index p (IV) ⋮ 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)

Cites Work

• On a special class of \(p\)-groups
• A theorem on metabelian p-groups and some consequences
• 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.
• Application of modules over a dyad for the classification of finite \(p\)-groups possessing an Abelian subgroup of index \(p\) and of pairs of mutually annihilating operators
• Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). II.
• 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
• Über das Produkt von paarweise vertauschbaren zyklischen Gruppen
• Finite p-groups with a minimal non-abelian subgroup of index p (V)
• Generalizations of Certain Elementary Theorems on p -Groups
• Finite p-Groups All of Whose Subgroups of Index p² Are Abelian
• Finite p-groups with a minimal non-abelian subgroup of index p (IV)
• Endliche Gruppen I
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