Wielandt’s criterion for the subnormality of a subgroup of a finite group is developed. For a set \(\pi=\{p_{1},p_{2},\mathinner{\ldotp\ldotp\ldotp},p_{n}\}\) and a partition \(\sigma=\{\{p_{1}\},\{p_{2}\},\mathinner{\ldotp\ldotp\ldotp},\{p_{n}\},\{\pi\}^ {\prime}\}\), it is proved that a subgroup \(H\) is \(\sigma\)-subnormal in a finite group \(G\) if and only if it is \(\{\{p_{i}\},\{p_{i}\}^{\prime}\}\)-subnormal in \(G\) for every \(i=1,2,\mathinner{\ldotp\ldotp\ldotp},n\). In particular, \(H\) is subnormal in \(G\) if and only if it is \(\{\{p\},\{p\}^{\prime}\}\)-subnormal in \(\langle H,H^{x}\rangle\) for every prime \(p\) and any element \(x\in G\).

开发了有限群的子群的次正规性的 Wielandt 判据。对于集合\(\pi=\{p_{1},p_{2},\mathinner{\ldotp\ldotp\ldotp},p_{n}\}\)和分区\(\sigma=\{\ {p_{1}\},\{p_{2}\},\mathinner{\ldotp\ldotp\ldotp},\{p_{n}\},\{\pi\}^ {\prime}\} \)，证明子群 \(H\)在有限群\(G \) 中是\(\sigma\) -次正规 当且仅当它是\(\{\{p_{i}\} ,\{p_{i}\}^{\prime}\}\) - 在 \(G\) 中对于每个\(i=1,2,\mathinner{\ldotp\ldotp\ldotp},n\) . 特别地，  \(H\)在\(G\) 中是次正规的 当且仅当它是\(\{\{p\},\{p\}^{\prime}\}\) -  \(\langle H,H^{x}\rangle\)对于每个素数 \(p\)和任何元素\(x\in G\)。