Derived subgroups and centers of capable groups

DOI10.1090/S0002-9939-01-05888-9zbMath0977.20014OpenAlexW1669860262MaRDI QIDQ2723479

I. M. Isaacs

Publication date: 5 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05888-9

zbMATH Keywords

centerscapable groupsderived subgroupscentral factor groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Series and lattices of subgroups (20D30) Finite nilpotent groups, (p)-groups (20D15)

Related Items (20)

On the Schur Lie-multiplier and Lie-covers of Leibniz n-algebras ⋮ On the orders of generators of capable p-groups ⋮ Bounds for the dimension of the center factor in capable nilpotent Lie algebras of class two ⋮ The commutator subgroup of a pair of groups ⋮ Capable \(n\)-Lie algebras and the classification of nilpotent \(n\)-Lie algebras with \(s(A) = 3\) ⋮ Bounds for the index of the centre in capable groups ⋮ An upper bound for the index of the center in capable groups with finite cyclic derived subgroups ⋮ On finite groups whose derived subgroup has bounded rank. ⋮ On capable groups of order p2q ⋮ Central Quotient Versus Commutator Subgroup of Groups ⋮ On the capability of finitep-groups with derived subgroup of orderp ⋮ A converse of Baer's theorem. ⋮ Generalizing a theorem of P. Hall on finite-by-nilpotent groups ⋮ Finite groups with a given absolute central factor group. ⋮ Categorizing finite p-groups by the order of their non-abelian tensor squares ⋮ A remark on the converse of Baer's theorem for Lie algebras ⋮ Capable 2-Generator 2-Groups of Class Two ⋮ Finite groups which are c-absolute central factor group and the union of Ac-centralizers ⋮ Classification of finite \(p\)-groups by the size of their Schur multipliers ⋮ On the q-capability of groups

Cites Work

• Nilpotent groups of class two that can appear as central quotient groups
• Group extensions, representations, and the Schur multiplicator
• On finite \(p\)-groups with cyclic commutator subgroup
• Automorphisms fixing elements of prime order in finite groups
• Eine Verallgemeinerung der invarianten Untergruppen
• Class two nilpotent capable groups

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