Covering numbers of groups

Abstract: Given a group $G$, $G$ can be expressed as the set-theoretical union of proper subgroups as long as $G$ is not cyclic. Assuming $G$ is the union of finitely many proper subgroups, we define the covering number of $G$, denoted by $\sigma(G)$, to be the minimum number of proper subgroups required in such a union. This begs the question: which integers are covering numbers of finite groups? This talk will be about joint work with Martino Garonzi and Luise-Charlotte Kappe in our attempts to answer this question, and the material in this talk should be accessible to undergraduate students.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Comments: Password: the order of the alternating group $A_8$.

GAG seminar

Series comments: Description: Non-specialized research seminar