Tue, 15 February 2022, 1 pm MST

The number of subdirect powers of an finite algebraic structure is a question that has appeared at various points in recent history. The situation is known in full for groups, and to some extent in semigroups. We answer the question for unary algebras, and look at how the situation is more complicated for infinite algebras. We then discuss what these results can tell us about the general question, and how it ties into other topics such as boolean separation.