On varieties arising from the solution of the restricted Burnside problem

DOI10.1016/S0022-4049(01)00115-3zbMath1007.20025MaRDI QIDQ1612112

P. V. Shumyatskij

Publication date: 22 August 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

varieties of groupslocally finite groupslocally nilpotent groupsmultilinear commutatorsverbal subgroupsgroup wordsrestricted Burnside problemdimension subgroupsHirsch-Plotkin heightLazard-Zassenhaus Lie algebrasLie PI-algebras

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Generalizations of solvable and nilpotent groups (20F19) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Associated Lie structures for groups (20F40)

Related Items (10)

On varieties of groups satisfying an Engel type identity. ⋮ On bounded conciseness of words in residually finite groups ⋮ Engel values in residually finite groups. ⋮ Commutators in residually finite groups. ⋮ Multilinear commutators in residually finite groups. ⋮ On locally graded groups with a word whose values are Engel ⋮ The restricted Burnside problem for multilinear commutators ⋮ Strong conciseness in profinite groups ⋮ ON THE EXPONENT OF A VERBAL SUBGROUP IN A FINITE GROUP ⋮ Words of Engel type are concise in residually finite groups

Cites Work

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• Identities for Lie algebras of pro-\(p\) groups
• Bounding the exponent of a finite group with automorphisms
• Strong finiteness conditions in locally finite groups
• On the p -Length of p -Soluble Groups and Reduction Theorems for Burnside's Problem
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• A (locally nilpotent)-by-nilpotent variety of groups
• Verbal subgroups in residually finite groups
• Applications of Lie ring methods to group theory
• Sur les groupes nilpotents et les anneaux de Lie

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