On a problem of P. Hall for Engel words.

DOI10.1007/S00013-011-0312-8zbMath1236.20044OpenAlexW2138907334MaRDI QIDQ652229

Alireza Abdollahi, Francesco G. Russo

Publication date: 14 December 2011

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

Full work available at URL: https://doi.org/10.1007/s00013-011-0312-8

zbMATH Keywords

numbers of generatorsfiniteness conditionsEngel wordsmarginal subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Engel conditions (20F45)

Related Items (9)

ON A PROBLEM OF P. HALL FOR ENGEL WORDS II ⋮ On conciseness of some commutator words ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On bounded conciseness of Engel-like words in residually finite groups ⋮ Engel groups in bath - ten years later ⋮ On finiteness of verbal subgroups ⋮ Embeddings of \(n\)-Engel marginal subgroups in compact groups ⋮ Words of Engel type are concise in residually finite groups

Cites Work

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• Verbal sets and cyclic coverings.
• On groups in which commutators are covered by finitely many cyclic subgroups.
• The converse of Schur's theorem
• Locally nilpotent 4-Engel groups are Fitting groups.
• Engelsche Elemente der Länge drei. (Engel elements of length three.)
• On locally finite 𝑝-groups satisfying an Engel condition
• Finiteness Conditions for Verbal Subgroups
• On three-Engel groups
• 4-ENGEL GROUPS ARE LOCALLY NILPOTENT

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