Tuesday, November 10th, 15:30, CRM Small Room
Speaker: Xaro Soler Escriva (Universitat d’Alacant)
Title: Languages recognized by finite supersoluble groups
Abstract: There exists a natural relationship between the classical theory of finite groups and the theory of formal languages. Given a finite alphabet A, one can easily associate to each regular language L of the free monoid A* an algebraic structure: its syntactic monoid. A regular language is a group language if its syntactic monoid is a group. Conversely, given a finite group G and a finite alphabet A, there exists a language of A* whose syntactic monoid is G (this is not true in
general if G is just a monoid).
After recalling the main ideas of the algebraic theory of regular languages, we will see some examples of languages recognized by finite groups. Then we will state Eilenberg’s theorem for varieties and the specific known results for abelian groups, nilpotent groups,
supersoluble groups, and soluble groups.
