Kuok Fai Chao

Centralizer Excess as an Obstruction to Carlson's Depth Conjecture

Let $G=\operatorname{SmallGroup}(128,859)$ and $k=\overline{k}$. The cohomology ring $H^*(G;k)$ has depth two, and we prove that the minimum quotient dimension of an associated prime is exactly three. Okuyama's theorem shows that an integer $r$ occurs as such a dimension exactly when there is an elementary abelian subg...