Modular invariant theory and cohomology algebras of extra-special p-groups

Pham Anh Minh

Vol. 124 (1986), No. 2, 345–363

DOI: 10.2140/pjm.1986.124.345

Abstract

Let W_n be the group of all translations on the vector space Z_pⁿ⁻¹. Every element of W_n is considered as a linear transformation on Z_pⁿ, i.e. W_n is identified to a subgroup of GL(n,Z_p). We have then a natural action of W_n on E(x₁,…,x_n;1) ⊗ P(y₁,…,y_n;2). The purpose of this paper is to determine a full system of invariants of W_n in this algebra. Using this result, we determine the image Im Res(A,G), for every maximal elementary abelian p-subgroup A of an extra-special p-group G.

Mathematical Subject Classification 2000

Primary: 20J05

Milestones

Received: 7 July 1983

Published: 1 October 1986