On finite \(p\)-groups with cyclic commutator subgroup

DOI10.1007/BF01899434zbMath0515.20014OpenAlexW2018198670MaRDI QIDQ1051719

Ying Cheng

Publication date: 1982

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01899434

zbMATH Keywords

inner automorphismsfinite \(p\)-groupscentermodular subgroup latticescentral products of 2-generator groupscyclic commutator subgroup

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Finite nilpotent groups, (p)-groups (20D15) Products of subgroups of abstract finite groups (20D40)

Related Items (24)

On the Norm and Wielandt Series in Finite Groups ⋮ The structure of groups with cyclic commutator subgroups indecomposable to a subdirect product of groups ⋮ Groups whose lattice of centralizers is a sublattice of the subgroup lattice ⋮ Finite \(p\)-groups with a cyclic commutator subgroup ⋮ An upper bound for the index of the center in capable groups with finite cyclic derived subgroups ⋮ On semicomplete finite \(p\)-groups ⋮ Class-preserving automorphisms of finite \(p\)-groups. II ⋮ On group invariants determined by modular group algebras: even versus odd characteristic ⋮ Central Quotient Versus Commutator Subgroup of Groups ⋮ Unnamed Item ⋮ Subgroups of powerful groups. ⋮ Integral of groups ⋮ On class preserving automorphisms of groups. ⋮ Derived subgroups and centers of capable groups ⋮ A note on the Chermak–Delgado lattice of a finite group ⋮ ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS ⋮ On \(IA\)-automorphisms that fix the centre element-wise. ⋮ Finite groups ⋮ On nilpotency of the group of outer class-preserving automorphisms of a group ⋮ On the Probability That an Automorphism Fixes a Group Element ⋮ Finite $2$-groups of class $2$ with a specific automorphism group ⋮ On finite p-groups with few normal subgroups ⋮ On Finitep-Groups Whose Central Automorphisms are all Class Preserving ⋮ Automorphisms of \(p\)-groups with cyclic commutator subgroup

Cites Work

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• Endliche Gruppen, in denen alle das Zentrum enthaltenden Untergruppen Zentralisatoren sind
• On p-groups with a cyclic commutator subgroup
• On Conditions for Commutators to Form a Subgroup
• Odd order nilpotent groups of class two with cyclic centre

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