Wielandt series and defects of subnormal subgroups in finite soluble groups (Q1199655)

While \textit{R. A. Bryce} and \textit{J. Cossey} [J. Lond. Math. Soc., II. Ser. 40, No. 2, 244-256 (1989; Zbl 0734.20010)] have shown that there is a bound on the derived length of a soluble group in terms of its Wielandt length, a highlight of the present article is the following result (Corollary 2 of Theorem 2): Let \(wl(G)\), \(l(G)\) and \(b(G)\) denote the Wielandt length, the Fitting length and the maximum of the subnormal defects of a group \(G\), respectively. Then there exists a function \(f:\mathbb{N}\times\mathbb{N}\to\mathbb{N}\) such that every soluble group \(G\) satisfies the inequality \(wl(G)\leq f(l(G),b(G))\).