Abstract.This paper proves the Alperin's weight conjecture for the finite unitary groups when the characteristic r of modular representation is odd. Moreover, this paper proves the conjecture for finite odd dimensional special orthogonal groups and gives a combinatorial way to count the number of weights, block by block, for finite symplectic and even dimensional special orthogonal groups when r and the defining characteristic of the groups are odd.

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We present a new strategy which exploits both the maximal and p-local subgroup structure of a given finite simple group in order to decide the Alperin and Dade conjectures for this group. We demonstrate the computational effectiveness of this approach by using it to verify these conjectures for the Conway simple group Co . ᮊ