turkmath.org

The Baer-Suzuki Theorem states that if $p$ is a prime, $x$ is a $p$-element in a finite group $G$ and $< x, x^g >$ is a $p$-group for every element $g$ of $G$, then the conjugacy class of $x$ in $G$ lies in a normal $p$-subgroup of $G$. In this talk, we present a very nice application of this theorem and using this we show that for a finite group $G$ with a semidihedral subgroup $P$, the Scott module $Sc(G,P)$ is Brauer indecomposable. This is a joint work with Shigeo Koshitani.