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Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups. (arXiv:1706.09572v1 [math.RT])
来源于:arXiv
Answering a question of P\'alfy and Pyber, we first prove the following
extension of the k(GV)-Problem: Let G be a finite group and A\le Aut(G) such
that (|G|,|A|)=1. Then the number of conjugacy classes of the semidirect
product GA is at most |G|. As a consequence we verify Brauer's k(B)-Conjecture
for pi-blocks of pi-separable groups which was proposed by Y. Liu. On the other
hand, we construct a counterexample to a version of Olsson's Conjecture for
pi-blocks which was also introduced by Liu. 查看全文>>