Sui gruppi simplettici finitari

We prove that finitary symplectic group FSp(V, f) is a simple group, provided (V, f) is a regular symplectic space of infinite dimension over a field of characteristic 2. On the other hand, when (V, f) is not regular, FSp(V, f) cannot be simple because it contains FSp₀(V, f), the normal subgroup of elements of FSp(V, f) acting trivially on rad(V, f), as a normal subgroup. In the non-regular case we show that even FSp₀(V, f) is not a simple group.