Let G be a finite group. A subgroup H of G is called a \({\mathbb {P}}\)-subnormal subgroup whenever \(H=G\) or there exists a chain of subgroups \(H=H_0\le H_1\le \cdots \le H_t=G\) such that \(|H_i:H_{i-1}|\) is a prime for every \(i\in \{1, 2, \ldots t\}\). In the present paper, we study finite groups in which some 2-maximal subgroups or cyclic subgroups are \({\mathbb {P}}\)-subnormal subgroups. Several conditions for G to possess an ordered Sylow tower of supersolvable type are given.

中文翻译：

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$$ {\ mathbb {P}} $$ P-次正规子群和有限群的结构

令G为一个有限群。每当\（H = G \）或存在一连串的子组\（H = H_0 \ le H_1 \ le \ cdots \时，G的子组H称为\（{\ mathbb {P}} \）-次正规子组。 H_t = G \）使得\（| H_i：H_ {i-1} | \）是每个\（i \ in \ {1，2，\ ldots t \} \）的素数。在本文中，我们研究了其中2个最大子群或循环子群为\（{\ mathbb {P}} \）-次正规子群的有限群。给出了G具有超可解类型的有序Sylow塔的几个条件。