FINITARY SYMPLECTIC GROUPS

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 not-equal 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.