4-ENGEL GROUPS ARE LOCALLY NILPOTENT

DOI10.1142/S0218196705002475zbMath1087.20029MaRDI QIDQ5703668

M. R. Vaghan-Lee, George Havas

Publication date: 8 November 2005

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

zbMATH Keywords

finitely generated groupsEngel groupslocally nilpotent groupscommutators

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) Software, source code, etc. for problems pertaining to group theory (20-04) Commutator calculus (20F12) Engel conditions (20F45)

Related Items (24)

On Non-Abelian Tensor Analogues of 3-Engel and 4-Engel Groups ⋮ A Note on Conciseness of Engel Words ⋮ The local nilpotence theorem for 4-Engel groups revisited ⋮ Groups that are Pairwise Nilpotent ⋮ ON A PROBLEM OF P. HALL FOR ENGEL WORDS II ⋮ Engel groups. III. ⋮ On \((\mathrm{n} + \frac 12)\)-Engel groups ⋮ On the exponent of Bogomolov multipliers ⋮ How to Tell if a Group Law Entails Virtual Nilpotence: Postscript ⋮ ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY ⋮ Unnamed Item ⋮ On a problem of P. Hall for Engel words. ⋮ Groups which satisfy a Thue–Morse identity ⋮ BURNSIDE-TYPE PROBLEMS RELATED TO SOLVABILITY ⋮ GROUP ALGEBRAS WHOSE UNIT GROUP IS LOCALLY NILPOTENT ⋮ SCHUR MULTIPLIERS OF n-ENGEL GROUPS ⋮ A NOTE ON THE LOCAL NILPOTENCE OF 4-ENGEL GROUPS ⋮ Unipotent automorphisms of solvable groups ⋮ Detecting laws in power subgroups ⋮ Algorithmic problems in Engel groups and cryptographic applications ⋮ Some remarks on unipotent automorphisms ⋮ RIGHT 4-ENGEL ELEMENTS OF A GROUP ⋮ On 4-Engel Groups ⋮ CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL

Uses Software

• Magma

Cites Work

• Verifying nilpotence
• Presentations of groups and monoids
• The Magma algebra system. I: The user language
• Locally nilpotent 4-Engel groups are Fitting groups.
• On \(4\)-Engel groups
• Engel-4 Groups of Exponent 5. II. Orders
• Engel-4 Groups of Exponent 5
• On locally finite 𝑝-groups satisfying an Engel condition
• TWO GENERATOR 4-ENGEL GROUPS
• Third Engel groups and the Macdonald-Neumann conjecture
• On three-Engel groups
• A NOTE ON THE LOCAL NILPOTENCE OF 4-ENGEL GROUPS

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