Some remarks concerning degree zero complete cohomology (Q2707506)

Let \(\widehat H^*(G,R)\) be the complete cohomology of a group \(G\) with coefficients in a commutative ring \(R\). \textit{A.~Adem} and \textit{J.~F.~Carlson} [J. Pure Appl. Algebra 66, No. 2, 111-120 (1990; Zbl 0822.20053)] asked for the extra cyclic summands of \(\widehat H^*_0(G,\mathbb{Z})\).NEWLINENEWLINENEWLINEThe authors give a group-theoretic description of \(\widehat H^*_0(G,\mathbb{F}_p)\) modulo its nilradical, where \(\mathbb{F}_p\) is the prime field. At the end, examples of discrete groups for which \textit{D.~Quillen}'s theorem [Ann. Math., II. Ser. 94, 573-602 (1971; Zbl 0247.57013)] does not hold are constructed.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00041].