Direct and subdirect products in combinatorial algebra, groups and semigroups

Abstract: For a while now, Peter Mayr and I have been looking at properties of direct and subdirect products in algebra, often motivated by some well known or particularly nice results from combinatorial group theory. The topics include finite generation, finite presentability, residual finiteness, infinite subdirect powers, etc. A fairly rich landscape has emerged over the years. Perhaps unsurprisingly the most general results can be obtained in the context of congruence permutable or modular varieties. This then leaves semigroups outside, and I have been working on such questions in parallel with some of my PhD students. In this talk I will try to sketch this landscape, not so much by means of a systematics introduction, but a few selected strands, results and comparisons.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.