Let $\sigma=\{\pi_i | i\in I$ and $\pi_i\cap\pi_j=\emptyset$ for all $i\neqj\}$ be a partition of the set of all primes into mutually disjoint subsets. Inthis paper we considered subgroups that permutes with given sets of$\pi_i$-maximal subgroups for all $\pi_i\in \sigma$. In particular we showedthat such subgroups forms a sublattice of the lattice of all subgroups of afinite group. As corollaries we obtained some well known results about$S$-permutable subgroups.
展开▼
机译：让$ \ sigma = \ {\ pi_i |对于所有$ i \ neqj \} $，i \ in I $和$ \ pi_i \ cap \ pi_j = \ emptyset $是所有素数集合的分区，成为互不相交的子集。在本文中，我们考虑了在给定的$ \ pi_i $-最大子组的情况下对\ sigma $中所有$ \ pi_i \进行置换的子组。特别地，我们证明了这些子群形成了一个有限群所有子群的晶格的一个子格。作为推论，我们获得了一些有关$ S $可置换子组的著名结果。
展开▼
