CONCISENESS OF COPRIME COMMUTATORS IN FINITE GROUPS

DOI10.1017/S0004972713000361zbMath1295.20017arXiv1303.1584OpenAlexW2114410974MaRDI QIDQ5409874

Anitha Thillaisundaram, Cristina Acciarri, P. V. Shumyatskij

Publication date: 15 April 2014

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.1584

zbMATH Keywords

finite groupsverbal subgroupscoprime commutatorsgroup wordspowers of commutatorsconcise wordslower central wordsderived words

Mathematics Subject Classification ID

Special subgroups (Frattini, Fitting, etc.) (20D25) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12)

Related Items (13)

Nilpotent residual of fixed points ⋮ Strong conciseness of coprime and anti-coprime commutators ⋮ Finite-by-nilpotent groups and a variation of the BFC-theorem ⋮ On finite groups in which coprime commutators are covered by few cyclic subgroups. ⋮ Strong conciseness of coprime commutators in profinite groups ⋮ Nilpotent residual of a finite group ⋮ A sufficient condition for nilpotency of the nilpotent residual of a finite group ⋮ BOUNDING THE ORDER OF THE NILPOTENT RESIDUAL OF A FINITE GROUP ⋮ Engel sinks of fixed points in finite groups ⋮ FITTING SUBGROUP AND NILPOTENT RESIDUAL OF FIXED POINTS ⋮ Coprime commutators in finite groups ⋮ On groups in which Engel sinks are cyclic ⋮ Nilpotent residual and fitting subgroup of fixed points in finite groups

Cites Work

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• The Ore conjecture.
• Coprime commutators in \(\mathrm{PSL}(2,q)\).
• Outer commutator words are uniformly concise
• A focal subgroup theorem for outer commutator words
• Groups with bounded verbal conjugacy classes
• Finiteness Conditions for Verbal Subgroups
• On Outer-Commutator Words

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