Definition:Length of Group
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Definition
Let $G$ be a finite group.
The length of $G$ is the length of a composition series for $G$.
That is, the length of $G$ is the number of factors in a composition series for $G$ (not including $G$ itself).
The length of $G$ can be denoted $\map l G$.
By the Jordan-Hölder Theorem, all composition series for $G$ have the same length.
Therefore, the length of a finite group $G$ is well-defined.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 73 \beta$