Tue, 23 Sep 2025, 1:25 pm MT
Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring), and let B be the countable atomless Boolean algebra.
We show that the automorphism groups of filtered Boolean powers of A by B have ample generics, which gives a new proof of our previous results that these groups have the small index property, uncountable cofinality and the Bergman property.
This is joint work with Nik Ruskuc.