On a certain ideal of Külshammer in the centre of a group algebra (Q5953404)

Let \(G\) be a finite group, and let \(F\) be an algebraically closed field of characteristic \(p>0\). The Reynolds ideal \(R\) of the center \(Z(FG)\) of the group algebra \(FG\) is defined as the \(F\)-span of all \(p'\)-section sums of \(G\). It is known that \(R^2=E_0\) where \(E_0\) is the \(F\)-span of all block idempotents of defect 0 in \(FG\). Let \(N:=p\) if \(p\) is odd, and let \(N:=4\) if \(p=2\). For a conjugacy class \(K\) of \(G\), let \(\Omega K\) be the set of all \(g\in G\) such that \(g^N\in K\). Moreover, let \(I\) be the \(F\)-space spanned by all sums \((\Omega K)^+\). Then \(I\) is an ideal of \(Z(FG)\) considered earlier by this reviewer, and \(I\) contains \(R\). The author shows that \(I^2=E_0\).