Subsets of groups: rational and context-free

Rational and recognizable subsets of groups are part of an important connection between the theory of formal languages and algebra. The corresponding context-free concepts  (algebraic and context-free subsets) can also be used to deduce algebraic properties of the group.

In this talk, we will explore rational, recognizable, algebraic and context-free subsets of subgroups of a given group, presenting an answer to a question of Herbst: if H is a subgroup of G and K is an algebraic subset of G contained in H, is K an algebraic subset of H?