The principal 3-blocks of the 3-dimensional projective special unitary groups in non-defining characteristic

In modular representation theory of finite groups., there is a well-known a nd important conjecture due to M. Broue. He has conjectured that, for a pri me p, if a finite group G has an abelian Sylow p-subgroup P, then the princ ipal p-blocks of G and the normalizer NG(P) of P in G would be derived equi valent. It is shown here that, the Broue's conjecture is true for a prime 3 and for the projective special unitary group G = PSU(3, q(2)) for a power q of a prime satisfying q equivalent to 2 or 5 (mod 9). In this case such a G has elementary abelian Sylow 3-subgroups of order 9.