Polynomial Identities in Graded Group Rings, Restricted Lie Algebras and p-Adic Analytic Groups

DOI10.2307/2154332zbMath0797.16031OpenAlexW4239548074WikidataQ115229202 ScholiaQ115229202MaRDI QIDQ4695378

Aner Shalev

Publication date: 19 October 1994

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2154332

zbMATH Keywords

topological groupfiltrationLie groupLie algebrasassociated graded ringrestricted Lie algebragroup ringpolynomial identity\(p\)-adic fieldfinitely generated groupaugmentation idealpro-\(p\)-completion\(p\)-adic analyticanalyticity criterion

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Universal enveloping (super)algebras (17B35) Graded rings and modules (associative rings and algebras) (16W50) General properties and structure of other Lie groups (22E20) Limits, profinite groups (20E18) Associated Lie structures for groups (20F40) Identities other than those of matrices over commutative rings (16R40)

Related Items (18)

Completion of restricted Lie algebras ⋮ Group algebras and enveloping algebras with nonmatrix and semigroup identities ⋮ Homological finiteness conditions for pro-pgroups ⋮ On profinite groups with automorphisms whose fixed points have countable Engel sinks ⋮ Power closure and the Engel condition ⋮ Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity ⋮ Strong conciseness of Engel words in profinite groups ⋮ Lie solvable enveloping algebras of characteristic two ⋮ Characterization of \(p\)-adic analytic groups in terms of wreath products ⋮ Infinitesimally PI radical algebras ⋮ On the Lie algebra of skew-symmetric elements of an enveloping algebra ⋮ Character degrees of \(p\)-groups and pro-\(p\) groups. ⋮ Compact groups in which all elements have countable right Engel sinks ⋮ Identities of Group Algebras ⋮ Profinite groups with an automorphism whose fixed points are right Engel ⋮ Analytic pro-\(p\) groups and their graded group rings ⋮ Compact groups with countable Engel sinks ⋮ Generalised nilpotence conditions inn-engel lie algebras

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