We study the relationships between the properties of nonperiodic groups and the norms of their decomposable subgroups. The influence of restrictions imposed on the norms of decomposable subgroups and on the properties of the group is analyzed under the condition that this norm is non-Dedekind and locally nilpotent. We also describe the structure of nonperiodic locally soluble groups for which the norm of decomposable subgroups possesses the indicated properties.

中文翻译：

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具有可分解子群的非戴德金局域幂零范数的非周期局域可解群

我们研究了非周期群的性质与其可分解子群的范数之间的关系。在该范数非戴德金且局部幂零的情况下，分析了限制对可分解子群的范数和群的性质的影响。我们还描述了非周期性局部可溶群的结构，其中可分解子群的范数具有指定的特性。