Modular representation analysis of sporadic finite simple groups by computers

利用Fong-Reynolds关于奇素数特征的定理，计算了零星单群J_4的极大子群的不可约Brauer特征标。利用这一结果，我们可以确定不属于主块的零星单群J_4的几乎不可约特征。利用J_4的这些不可约的Brauer特征标证明了J_4的Broue猜想是肯定的。此外，还对主块的射影特征字的计算进行了研究。

Irreducible Brauer characters of maximal subgroups of the sporadic simple group J_4 are calculated by Fong-Reynolds's theorem on characteristic of all odd primes. With this results, we can determine the almost irreducible characters of the sporadic simple group J_4 which is not belonged in the principal blocks. These irreducible Brauer characters of J_4 are used to prove that the Brou¶e conjecture for J_4 is in the affirmative. Moreover the calculation of projective characters in the principal block is also stared.