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
 |
(1)
|
is one composition series and
 |
(2)
|
is another, then 
,
and corresponding to any composition quotient group 
, there is a composition quotient
group 
such that
 |
(3)
|
This theorem was proven in 1869-1889.
See also
Butterfly Lemma,
Composition Series,
Finite Group,
Isomorphic
Groups
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References
Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 26, 1993.Scott, W. R.
§2.5.8 in Group
Theory. New York: Dover, p. 37, 1987.Referenced on Wolfram|Alpha
Jordan-Hölder Theorem
Cite this as:
Weisstein, Eric W. "Jordan-Hölder Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Jordan-HoelderTheorem.html
Subject classifications
