Bounds for the index of the centre in capable groups

DOI10.1090/S0002-9939-05-07663-XzbMath1088.20018OpenAlexW1489754080MaRDI QIDQ5313322

Károly Podoski, Balázs Szegedy

Publication date: 29 August 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-07663-x

zbMATH Keywords

centrescapable groupscommutator subgroupnumerical connections

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Finite nilpotent groups, (p)-groups (20D15) Derived series, central series, and generalizations for groups (20F14)

Related Items (10)

Bounds for the dimension of the center factor in capable nilpotent Lie algebras of class two ⋮ Generalizing a Rank Analogue of Hall's Theorem ⋮ 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 \(c\)-capability and \(n\)-isoclinic families of a specific class of groups ⋮ Central Quotient Versus Commutator Subgroup of Groups ⋮ Second centralizers and autocommutator subgroups of automorphisms ⋮ Generalizing a theorem of P. Hall on finite-by-nilpotent groups ⋮ Finite groups with a given absolute central factor group. ⋮ AN APPROACH TO CAPABLE GROUPS AND SCHUR’S THEOREM

Cites Work

• Nilpotent groups of class two that can appear as central quotient groups
• Multiplicators and groups with finite central factor-groups
• Derived subgroups and centers of capable groups
• Bounds in groups with finite abelian coverings or with finite derived groups
• Some Explicit Bounds in Groups with Finite Derived Groups
• Groups covered by an infinite number of abelian subgroups

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