Let E be an elementary abelian p-group of order q=pn. Let W be a faithful indecomposable representation of E with dimension 2 over a field k of characteristic p, and let V=Sm(W)with m<q. We prove that the rings of invariants k[V]E are generated by elements of degree ≤q and relative transfers. This extends recent work of Wehlau  on modular invariants of cyclic groups of order p. If m<p we prove that k[V]E is generated by invariants of degree ≤2q−3, extending a result of Fleischmann, Sezer, Shank and Woodcock  for cyclic groups of order p. Our methods are primarily representation-theoretic, and along the way we prove that for any d<q with d+m≥q, ⁎Sd(V⁎) is projective relative to the set of subgroups of E with order ≤m, and that the sequence ⁎Sd(V⁎)d≥0 is periodic with period q, modulo summands which are projective relative to the same set of subgroups. These results extend results of Almkvist and Fossum  on cyclic groups of prime order.
Bibliographical noteSpecial thanks go to Professor David Benson a number of invaluable conversations at the genesis of this work. Thanks also to Dr. Müfit Sezer for his assistance with the proof of Proposition 4.3, and an anonymous referee for some helpful remarks.
- modular representation theory
- invariant theory
- elementary abelian p-groups
- symmetric powers
- relative stable module category