We study groups in which each subnormal subgroup is commensurable with a normal subgroup. Recall that two subgroups 𝐻 and 𝐾 are termed commensurable if H∩KH\cap K has finite index in both 𝐻 and 𝐾. Among other results, we show that if a (sub)soluble group 𝐺 has the above property, then 𝐺 is finite-by-metabelian, i.e., G′′G^{\prime\prime} is finite.

中文翻译：

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每个次正态子组与某个正态子组相称的组

我们研究了每个亚正常亚组与正常亚组相称的组。回想一下，如果 H∩KH\cap K 在 𝐻 和 𝐾 中都具有有限索引，则两个子群 𝐻 和 𝐾 被称为可公度的。在其他结果中，我们表明，如果（亚）可溶群 𝐺 具有上述性质，则 𝐺 是有限元元的，即 G′′G^{\prime\prime} 是有限的。