Invariants of modular groups (Q2470368)

The author proves several properties of modular representations of a finite group, especially the polynomial and Cohen-Macaulay properties of the invariant ring. For example, he proves the Hilbert ideal conjecture for vector invariant rings of abelian reflection \(p\)-groups. He also studies the relationships between the invariant rings of a group and its subgroups. He shows that over a finite field, if an affine group contains all translations, then the invariant ring is isomorphic to the invariant ring of a linear group.