Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: Aner Shalev
Journal: Trans. Amer. Math. Soc. 337 (1993), 451-462
MSC: Primary 16R99; Secondary 16S34, 16W50, 17B50, 20E18
DOI: https://doi.org/10.1090/S0002-9947-1993-1093218-X
MathSciNet review: 1093218
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be any finitely generated group, and let $K$ be a field of characteristic $p > 0$. It is shown that the graded group ring $\operatorname {gr}(KG)$ 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 ${\mathbb {Q}_p}$. The proof applies theorems of Lazard, Quillen and Passman, as well as results on Engel Lie algebras and on dimension subgroups in positive characteristic.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16R99, 16S34, 16W50, 17B50, 20E18

Retrieve articles in all journals with MSC: 16R99, 16S34, 16W50, 17B50, 20E18


Additional Information

Article copyright: © Copyright 1993 American Mathematical Society