Filters compatible with isomorphism testing

Maglione J. Filters compatible with isomorphism testing. Journal of Pure and Applied Algebra. 2021;225(3): 106528.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 can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings. (C) 2020 Elsevier B.V. All rights reserved