The converse of Schur's theorem

DOI10.1007/s00013-010-0106-4zbMath1197.20023OpenAlexW2071655091MaRDI QIDQ974642

Peyman Niroomand

Publication date: 4 June 2010

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

Full work available at URL: https://doi.org/10.1007/s00013-010-0106-4

zbMATH Keywords

finite groupscenterfinitely generated groupsnilpotent groupsSchur theoremcentral factorderived subgroup

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) General structure theorems for groups (20E34) Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) Local properties of groups (20E25)

Related Items (16)

Nilpotent groups related to an automorphism ⋮ Non-abelian tensor square of finite-by-nilpotent groups ⋮ The commutator subgroup of a pair of groups ⋮ On Schur’s theorem and its converses forn-Lie algebras ⋮ On the converse of a theorem of Schur. ⋮ The Schur multiplier of an n-Lie superalgebra ⋮ A generalization of a converse to Schur's theorem. ⋮ An upper bound for the index of the center in capable groups with finite cyclic derived subgroups ⋮ Characterizing nilpotent Lie algebras that satisfy the converse to the Schur theorem ⋮ Central Quotient Versus Commutator Subgroup of Groups ⋮ Some properties on \(\mathrm{IA}_{\mathrm{Z}}\)-automorphisms of groups ⋮ On a problem of P. Hall for Engel words. ⋮ A converse of Baer's theorem. ⋮ Second centralizers and autocommutator subgroups of automorphisms ⋮ Ensuring a Group is Weakly Nilpotent ⋮ A remark on the converse of Baer's theorem for Lie algebras

Cites Work

• On a theorem of Schur.
• On variants of a theorem of Schur.

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