On finite soluble groups (Q2535394)

The author proves two results. Theorem 1. If a Sylow \(p\)-subgroup of a finite \(p\)-soluble group \(G\) can be generated by \(d\) elements, then the \(p\)-length of \(G\) is at most \(d\). Theorem 2. If each Sylow subgroup of a finite soluble group \(G\) can be generated by \(d\) elements, then \(G\) can be generated by \(d+1\) elements. Reviewer's remark: Theorem 1 can be proved for all finite groups using the general definition of the \(p\)-length [see the reviewer, Math. USSR, Sb. 1(1967), 83--92 (1968); translation from Mat. Sb., n. Ser. 72(114), 97--107 (1967; Zbl 0179.32401)], and a theorem of \textit{P. Roquette} [J. Algebra 1, 342--346 (1964; Zbl 0166.28702)].