let $M$ be a finitely generated, commutative monoid.
What are in general the relations between $\mathrm{Aut}(M)$ and $\mathrm{Aut}(M^{\rm gp})$?
When is it true that $\mathrm{Aut}(M)$ determines $\mathrm{Aut}(M^{\rm gp})$?
let $M$ be a finitely generated, commutative monoid.
What are in general the relations between $\mathrm{Aut}(M)$ and $\mathrm{Aut}(M^{\rm gp})$?
When is it true that $\mathrm{Aut}(M)$ determines $\mathrm{Aut}(M^{\rm gp})$?