If $G$ is a group, the **chief series** of $G$ is a normal series
\[ \langle e\rangle=N_0 \lhd N_1 \lhd \cdots \lhd N_k=G\]
where each $N_{i+1}/N_i$ is a minimal normal subgroup of $G/N_i$.

The factor groups $N_{i+1}/N_i$ are each isomorphic to a product of some number of copies of a single simple group (which depends on $i$). These simple groups (together with their multiplicities) are the **composition factors** of $G$. While there may be many chief series for $G$, the set of composition factors is a well defined invariant.

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- Review status: reviewed
- Last edited by David Roe on 2021-09-29 01:40:55

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