Supernilpotent reducts of nilpotent algebras

Description

We show that every finite nilpotent Mal’cev algebra has a supernilpotent Mal’cev reduct, that is, a reduct that is a direct product of algebras of prime power order. Recall that every finite supernilpotent Mal’cev algebra is finitely based by work of Vaughan–Lee (1983) and Freese and McKenzie (1987). In his paper Vaughan–Lee also points out a particular nilpotent loop of size 12, which is not supernilpotent and hence not covered by their techniques. Using its supernilpotent reduct, we can now show that this loop is still finitely based. This is joint work with Michael Kompatscher and Patrick Wynne.

Period	24 Jun 2022
Event title	AAA 102 – Workshop on General Algebra
Event type	Conference
Location	HungaryShow on map