Applications of Lie ring methods to group theory

zbMath0973.20027arXiv1706.07963MaRDI QIDQ4762456

P. V. Shumyatskij

Publication date: 29 August 2001

Full work available at URL: https://arxiv.org/abs/1706.07963

zbMATH Keywords

soluble groupsnilpotent groupsautomorphismscentralizersperiodic groupslocally finite groupsEngel conditionscommutatorsresidually finite groupsderived lengths\(p\)-groupsLie ringsPI-algebrasrestricted Burnside problembinary finite groups

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Automorphisms of abstract finite groups (20D45) Automorphisms of infinite groups (20E36) Finite nilpotent groups, (p)-groups (20D15) Residual properties and generalizations; residually finite groups (20E26) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25) Commutator calculus (20F12) Engel conditions (20F45) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Associated Lie structures for groups (20F40) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (28)

Automorphisms of abelian Lie ring extensions ⋮ Advances on a construction related to the non-abelian tensor square of a group ⋮ Exponent of a finite group admitting a coprime automorphism ⋮ Arithmetically-free group-gradings of Lie algebras. II ⋮ On words that are concise in residually finite groups. ⋮ Lie algebra associated with the group of finitary automorphisms of \(p\)-adic tree. ⋮ Non-abelian tensor product of residually finite groups ⋮ Engel groups with an identity ⋮ Fixed points of coprime operator groups. ⋮ Bounded Engel elements in groups satisfying an identity ⋮ Profinite groups and centralizers of coprime automorphisms whose elements are Engel ⋮ On groups with automorphisms whose fixed points are Engel ⋮ On bounded conciseness of Engel-like words in residually finite groups ⋮ The non-abelian tensor square of residually finite groups ⋮ On profinite groups with Engel-like conditions. ⋮ Bounded Engel elements in residually finite groups ⋮ Engel groups in bath - ten years later ⋮ Profinite groups and the fixed points of coprime automorphisms. ⋮ Finiteness conditions for the non-abelian tensor product of groups ⋮ Profinite groups with restricted centralizers of commutators ⋮ Engel-like conditions in fixed points of automorphisms of profinite groups ⋮ Exponent of a finite group of odd order with an involutory automorphism ⋮ Profinite groups with an automorphism whose fixed points are right Engel ⋮ Bounded Engel elements in residually finite groups satisfying an identity ⋮ On residually finite groups satisfying an Engel type identity ⋮ On finite groups in which commutators are covered by Engel subgroups ⋮ On finite groups with automorphisms whose fixed points are Engel. ⋮ On varieties arising from the solution of the restricted Burnside problem

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