  We study generalized Kummer surfaces Km$_{3}(A)$, by which we mean the K3
surfaces obtained by desingularization of the quotient of an abelian surface
$A$ by an order $3$ symplectic automorphism group. Such a surface carries $9$
disjoint configurations of two smooth rational curves $C,C'$ with $CC'=1$. This
$9{\bf A}_{2}$-configuration plays a role similar to the Nikulin configuration
of $16$ disjoint smooth rational curves on (classical) Kummer surfaces. We
study the (generalized) question of T. Shioda: suppose that Km$_{3}(A)$ is
isomorphic to Km$_{3}(B)$, does that imply that $A$ and $B$ are isomorphic? We
answer by the negative in general, by two methods: by a link between that
problem and Fourier-Mukai partners of $A$, and by construction of $9{\bf
A}_{2}$-configurations on Km$_{3}(A)$ which cannot be exchanged under the
automorphism group.
