Polynomial identities in graded group rings, restricted Lie algebras and $p$-adic analytic groups
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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
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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