The composition length of a finite-length module or group is the number of simple factors in a composition series. The Jordan–Hölder theorem makes this independent of the chosen composition series.
A Jordan–Hölder factor is a simple quotient in a composition series. The Jordan–Hölder theorem says that the multiset of such factors is independent of the chosen composition series.
Any two composition series of a finite group or finite-length module have the same length and the same simple factors up to permutation and isomorphism.
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A **composition series** is a specific type of series in the context of group theory in mathematics, particularly in the study of finite groups. It provides a way to break down a group into simple components.
