The composition quotient groups belonging to two Composition Series of a Finite Group are, apart from their
sequence, Isomorphic in pairs. In other words, if

is one Composition Series and

is another, then , and corresponding to any composition quotient group , there is a composition quotient group such that

This theorem was proven in 1869-1889.

**References**

Lomont, J. S. *Applications of Finite Groups.* New York: Dover, p. 26, 1993.

© 1996-9

1999-05-25