Speaker: Prof.Xiuyun Guo (Shanghai University )

Title:The Coprime Action of Finite groups

Time: Sun, June.3, 2018 , PM:4:00-5:00.

Location: Room 4318, Building No.4, Wushan Campus

Abstract:

  Let Abe an elementary abelian $r$-group acting on a finite $r'$-group $G$. Suppose that the fixed-point group $\Cent_G(a)$ is supersolvable for each $a \in A^\#$. We show that $G$ is supersolvable if $|A|\geqslant r^4$ and that $G'\leqslant \FF_3(G)$ if $|A|\geqslant r^3$. Moreover, we prove some other results for cases when the fixed-point group $\Cent_G(a)$ is abelian, $p$-nilpotent or satisfies the Sylow tower property.