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Jordan–Hölder theorem
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Area of mathematics
Algebra
Group theory
Finite group theory
Composition series
Jordan–Hölder factor
Created
2026-09-28
Updated
2026-11-05
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Any two
composition series
of
a
finite group
or finite-
length
module
have the same
length
and the same simple factors
up to
permutation
and
isomorphism
.
Ancestors
(8)
Jordan–Hölder factor
Composition series
Finite group theory
Group theory
Algebra
Area of mathematics
Mathematics
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(24)
Brauer character basis theorem
Composition length
Exactly two composition series for a simple group times a prime cyclic group
Jordan–Hölder factor
Length of a module
Modular representation ring
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Schreier refinement theorem
Subdirect product of pairwise nonisomorphic simple modules
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Jordan-Holder Theorem
by
Ciro Santilli
40
Updated
2025-07-16
View more
Uniqueness
results for the
composition series
of
a
group
.
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