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Let $M$ be a symplectic symmetric space, and let $\imath : M \to V$ be anextrinsic symplectic symmetric immersion, i.e., $(V, \Omega)$ is a symplecticvector space and $\imath$ is an injective symplectic immersion such that foreach point $p \in M$, the geodesic symmetry in $p$ is compatible with thereflection in the affine normal space at $\imath(p)$. We show that theexistence of such an immersion implies that the transvection group of $M$ issolvable.

On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces