A proof of the Kegel-Wielandt conjecture on subnormal subgroups
Using the classification of the finite simple groups the author proves the following theorem which appears as a conjecture in papers of \textit{O. H. Kegel} [Math. Z. 78, 205-221 (1962; Zbl 0102.26802)] and \textit{H. Wielandt} [Proc. Symp. Pure Math. 37, 161-173 (1980; Zbl 0458.20024)]: Let \(G\) be a finite group and \(H\) a subgroup of \(G\). Then \(H\) is subnormal in \(G\) if and only if for all primes \(p\), every Sylow \(p\)-subgroup of \(G\) intersects \(H\) in a Sylow \(p\)-subgroup of \(H\).
scientific article; zbMATH DE number 4198308