Rewriting systems and group extensions

Abstract: The first examples of groups in a textbook are often as words in generators, subject to some easy rules. This seems nice and natural, but gets quickly abandoned once the groups involved become more complicated. A similar disappointment happens when introducing group extensions: Examples in textbooks never go beyond easy cases such as cyclic groups or split extensions. But this is not intended to whine about textbooks. Instead I want to show how a systematic approach to normal form words (namely confluent rewriting systems) can be used to describe group extension (and explicitly compute 2-cohomology), resulting in practically useful (and implemented!) algorithms.

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.