Let $G$ be a finite group with a fixed subset $A$. Put $$ S_r(A)=\{B\subseteq G : |AB|=|A||B|\; \& \; B \; \mbox{is inclusion-maximal with respect to this property}\} $$ $$ M_r(A)=\max\{|B| : B\in S_r(A) \} $$ $$ m_r(A)=\min\{|B| : B\in S_r(A) \} $$ ($S_\ell(A)$, $M_\ell(A)$ and $m_\ell(A)$ are defined analogously).
Now, I need a GAP code for evaluating $S_r(A)$, $M_r(A)$ and $m_r(A)$ ($\; S_\ell(A)$, $M_\ell(A)$ and $m_\ell(A)$).
Note. Always $S_r(A)\neq\emptyset$ and $$ M_r(A)=\max\{|B| : B\subseteq G \; \& \; |AB|=|A||B|\} $$ If $A\leq G$ then $M_r(A)=m_r(A)=M_\ell(A)=m_\ell(A)=|G:A|$.
(also see https://mathoverflow.net/questions/177747/factorization-of-a-finite-group-by-two-subsets)