Any two composition series of a finite group (or of a module of finite length) have the same length and, up to reordering and isomorphism, the same composition factors. Named for Camille Jordan and Otto Holder, it shows that a group's basic building blocks are uniquely determined.
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StatementAny two composition series of a given group are equivalent: they have the same composition length and the same composition factors, up to permutation and isomorphism. 1 Classification
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1. Jordan-Holder Theorem (Wikipedia, Composition Series Article)
Wikimedia FoundationComposition series article, Jordan-Holder theorem section
any two composition series of a given group are equivalent. That is, they have the same composition length and the same composition factors, up to permutation and isomorphism.
In Group: Group Theory, Article text
Nevertheless, a group of results known under the general name Jordan-Hölder theorem asserts that whenever composition series exist, the isomorphism classes of simple pieces (although, perhaps, not their location in the composition series in question) and their multiplicities are uniquely determined.
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