Year: 2018
Type: preprint
Abstract: Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring may be trivial or arbitrarily large. We determine properties of filters such that the Lie ring and group are in bijection. We prove that, under such conditions, every isomorphism between groups is induced by an isomorphism between graded Lie rings.
Source: arXiv (Cornell University)
Author: Maglione, Joshua
Institution: Bielefeld University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2802811296