Jordan-Hölder theorem

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Jordan-Hölder theorem

[zhȯr′dän′hu̇l·dər ‚thir·əm]
(mathematics)
The theorem that for a group any two composition series have the same number of subgroups listed, and both series produce the same quotient groups.
References in periodicals archive ?
By Jordan-Holder theorem (see [1] or [3]), we know the length of a composition series is a constant, only dependent on [??].
By Jordan-Holder theorem, we know the length of this composition series is a constant, dependent only on ([G.sub.1], [x.sub.1]).
(Jordan-Holder theorem) For a finite group G, the length of the composition series is a constant, only dependent on G.
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