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In the representation theory of finite groups, there is a well-known andimportant conjecture due to M. Brou\'e. He conjectures that, for any prime p,if a p-block A of a finite group G has an abelian defect group P, then A andits Brauer corresponding block A_N of the normaliser N_G(P) of P in G arederived equivalent (Rickard equivalent). This conjecture is called StrongVersion of Brou\'e's Abelian Defect Group Conjecture. In this paper, we provethat the strong version of Brou\'e's abelian defect group conjecture is truefor the non-principal 2-block A with an elementary abelian defect group P oforder 8 of the sporadic simple Conway group Co_3. This result completes theverification of the strong version of Brou\'e's abelian defect group conjecturefor all primes p and for all p-blocks of Co_3.

Brou\'e's abelian defect group conjecture holds for the sporadic simple Conway group Co_3