  In [9] Bogdan Nica presented an elementary proof of a result which says that
the relative elementary linear group with respect to a square of an ideal of
the ring is a subset of the true relative elementary linear group. The original
result was proved by J. Tits in [16] in the much general context of Chevalley
groups. In this paper we prove analogues of the result of Tits for linear
transvection group and symplectic transvection group. We also obtain an
elementary proof of a special case of the result by Tits, namely the case of
elementary symplectic group, using commutator identities for generators of this
group.
