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
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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 -