Algebra Seminar talk

Julius Jonušas
Universal words and sequences

Given a group or a semigroup, I am particularly interested in finding (preferably minimal) generating set of the group. However, every generating set of an uncountable group must be of the same cardinality as the group itself, in which case generating sets proved very little new information about the structure of the group. In this talk, I will introduce notions of universal words and universal sequences for groups and semigroups, and then show how universal sequences can be thought as an extension of the notion of generation.