On the nilpotency index of the radical of a group algebra. V
[For part IV cf. Math. J. Okayama Univ. 25, 35-42 (1983; Zbl 0514.16007).] Let K be a field of characteristic \(p>0\), let G be a finite p-solvable group, let J(KG) be the radical of the group algebra KG over K and let t(G) be the nilpotency index of J(KG). Mainly by direct calculation the author proves that if \(p=3\) and if G has a 3-Sylow subgroup of the type \(<x,y,c| \quad c^ 3=x^ 3=y^ 3=1,\quad x^ c=x,\quad y^ c=xy,\quad x^ y=x>\) then \(t(G)=9\). This settles a question, left open for \(p=3\), in the work of \textit{S. Koshitani} [J. Algebra 80, 134-144 (1983; Zbl 0507.16011)].
scientific article; zbMATH DE number 3863395