From Auslander-Buchsbaum theorem to invariant theory

The above A-B theorem states that a regular local commutative ring is a UFD (factorial).

This suggests analogous questions,and answers,for the centers of well known non-commutative algebras(e.g. the enveloping algebra of a finite dimensional Lie algebra).

This leads to questions in invariant theory of finite groups.

An unexpected upshot ,appears in the classification of finite subgroups G of GL(3,F),where char.F divides the order of G. We shall describe this path in some details.