Meaning of Jordan-Hölder theorem

Jor'dan-Höl'der the"orem

Pronunciation: ( jôr'dn-hel'dur), [key]
— Math. Math.
  1. 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.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.