Category:Definitions/Normal Series

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This category contains definitions related to Normal Series in the context of Group Theory.
Related results can be found in Category:Normal Series.

Let $G$ be a group whose identity is $e$.

A normal series for $G$ is a sequence of (normal) subgroups of $G$:

$\set e = G_0 \lhd G_1 \lhd \cdots \lhd G_n = G$

where $G_{i - 1} \lhd G_i$ denotes that $G_{i - 1}$ is a proper normal subgroup of $G_i$.