Dyer-Lashof operations on Tate cohomology of finite groups. (Q422125)

Let \(p\) be a prime number, \(G\) be a finite group and \(\widehat{H^*}(G,\mathbb F_p)\) be the Tate cohomology of \(G\). In this paper, the author constructs power operations of Dyer-Lashof type on \(\widehat{H^*}(G,\mathbb F_p)\) by exhibiting an \(E_\infty\)-operad action on \(\Hom(\mathcal P,\mathbb F_p)\) for a complete projective resolution \(\mathcal P\) of the trivial \(\mathbb F_p[G]\)-module \(\mathbb F_p\). He gives some properties and applications of these operations. In particular, he shows that they agree with the Steenrod operations on \(H^*(G,\mathbb F_p)\).