A subgroup \( A \) of a group \( G \) is \( G \)-permutable in \( G \) if for every subgroup \( B\leq G \) there exists \( x\in G \) such that \( AB^{x}=B^{x}A \). A subgroup \( A \) is hereditarily \( G \)-permutable in \( G \) if \( A \) is \( E \)-permutable in every subgroup \( E \) of \( G \) which includes \( A \). The Kourovka Notebook has Problem 17.112(b): Which finite nonabelian simple groups \( G \) possess a proper hereditarily \( G \)-permutable subgroup? We answer this question for the exceptional groups of Lie type. Moreover, for the Suzuki groups \( G\cong{{}^{2}\!\operatorname{B}_{2}}(q) \) we prove that a proper subgroup of \( G \) is \( G \)-permutable if and only if the order of the subgroup is 2. In particular, we obtain an infinite series of groups with \( G \)-permutable subgroups.

群\( G \)的子群\( A \ )在 \( G \)中是\( G \)可置换的，如果对于每个子群\( B\leq G \)存在\( x\in G \) )使得 \( AB^{x}=B^{x}A \)。子群\( A \)在 \( G \) 中遗传地 \( G \)是可置换的 ，如果 \( A \)在 \( G \)的 每个子群 \( E \)中是\( E \ )可置换的其中包括 \( A \)。 Kourovka 笔记本有问题 17.112(b)：哪些有限非阿贝尔单群\( G \)拥有适当的遗传性\(G\)-可置换子群？我们针对李型的特殊群体来回答这个问题。此外，对于铃木群 \( G\cong{{}^{2}\!\operatorname{B}_{2}}(q) \)我们证明 \( G \)的真子群 是\( G \) -可置换当且仅当子群的阶为 2 时。特别地，我们获得具有\( G \) -可置换子群的无穷级数群。