# Jordan-Hölder theorem

[jawr-dn-hel-der]

- the theorem that for any two composition series of a group, an isomorphism exists between the corresponding quotient groups of each series, taken in some specified order.

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## Origin of Jordan-Hölder theorem^{}

after M.E.C. Jordan and German mathematician Ludwig Otto Hölder (1859–1937)

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018