Degree of reductivity of a modular representation

Abstract

For a finite dimensional representation $V$ of a group $G$ over a field $F$, the degree of reductivity $\delta (G,V)$ is the smallest degree $d$ such that every nonzero fixed point $v\in V^G\setminus \{0\}$ can be separated from zero by a homogeneous invariant of degree at most $d$. We compute $\delta (G,V)$ explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian $p$-groups.

10 pages

References in corpus (2)

• Zero-separating invariants for finite groups
• Rings of invariants for modular representations of the Klein four group