  We prove that for an arbitrary $\varepsilon>0$ and any multiplicative
subgroup $\Gamma \subseteq \mathbf{F}_p$, $1\ll |\Gamma| \le p^{2/3
-\varepsilon}$ there are no sets $B$, $C \subseteq \mathbf{F}_p$ with $|B|,
|C|>1$ such that $\Gamma=B+C$. Also, we obtain that for $1\ll |\Gamma| \le
p^{6/7-\varepsilon}$ and any $\xi\neq 0$ there is no a set $B$ such that $\xi
\Gamma+1=B/B$.
