I know that if $H$ and $K$ are subgroups of a finite group $G$, then $|HK|=\frac{|H||K|}{|H\cap K|}$.
Is there a formula for $|\langle H\cup K\rangle|$, if $H$ and $K$ are nonempty subsets of a finite group $G$?
I know that if $H$ and $K$ are subgroups of a finite group $G$, then $|HK|=\frac{|H||K|}{|H\cap K|}$.
Is there a formula for $|\langle H\cup K\rangle|$, if $H$ and $K$ are nonempty subsets of a finite group $G$?