TY - JOUR

T1 - Polynomial identities in graded group rings, restricted lie algebras and p-adic analytic groups

AU - Shalev, Aner

PY - 1993/5

Y1 - 1993/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968473096&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1993-1093218-X

DO - 10.1090/S0002-9947-1993-1093218-X

M3 - Article

AN - SCOPUS:84968473096

SN - 0002-9947

VL - 337

SP - 451

EP - 462

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -