Chief series of a group (reviewed)

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.