Two subgroups A and B of a group G are called msp-permutable if the following statements hold: AB is a subgroup of G; the subgroups P and Q are mutually permutable, where P is an arbitrary Sylow p-subgroup of A and Q is an arbitrary Sylow q-subgroup of B, $${p\ne q}$$ . In the present paper, we investigate groups that are factorized by two msp-permutable subgroups. In particular, the supersolubility of the product of two supersoluble msp-permutable subgroups is proved.

中文翻译：

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关于具有可变因子子群的有限分解群

如果以下陈述成立，则群 G 的两个子群 A 和 B 称为 msp-permutable：AB 是 G 的子群；子群 P 和 Q 是相互可置换的，其中 P 是 A 的任意 Sylow p-子群，Q 是 B 的任意 Sylow q-子群 $${p\ne q}$$ 。在本文中，我们研究了由两个 msp-permutable 子群分解的群。特别地，证明了两个超溶 msp-置换子群的乘积的超溶性。