Polynomial identities in graded group rings, restricted lie algebras and p-adic analytic groups

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Let G be any finitely generated group, and let K be a field of chacteristic p > 0. It is shown that the graded group ring gr(KG) satisfies a nontrivial polynomial identity if and only if the pro-p completion of G is p-adic analytic, i.e. Can be given the structure of a Lie group over the p-adic field ℚp. The proof applies theorems of Lazard, Quillen and Passman, as well as results on Engel Lie algebras and on dimension subgroups in positive characteristic.

Original languageAmerican English
Pages (from-to)451-462
Number of pages12
JournalTransactions of the American Mathematical Society
Volume337
Issue number1
DOIs
StatePublished - May 1993

Fingerprint

Dive into the research topics of 'Polynomial identities in graded group rings, restricted lie algebras and p-adic analytic groups'. Together they form a unique fingerprint.

Cite this