The paper deals with subnormal and composition subgroups in the framework of weak congruence lattices of groups. Weak congruences of the composition subgroups of a group form a sublattice of the lattice of all weak congruences. We characterize normality and subnormality in purely lattice-theoretic terms. For a finite group G we prove: all subgroups of G are subnormal (i.e., G is nilpotent) if and only if the weak congruence lattice of G is lower semimodular.

中文翻译：

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有限幂等群的格表征

本文在弱同余格群的框架下处理次正规子群和组成子群。一个组的组成子组的弱同余会形成所有弱同余的点阵的子格。我们用纯晶格理论来描述正态性和次正态性。对于有限群G ^我们证明：的所有子组G ^是低于正常（即，G ^是幂零）当且仅当的弱一致性晶格ģ是低级semimodular。