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Jordan-Hölder decomposition theorem (Theorem)

Every finite group $ G$ has a filtration

$\displaystyle G \supset G_0 \supset \cdots \supset G_n = \{1\}, $
where each $ G_{i+1}$ is normal in $ G_i$ and each quotient group $ G_i/G_{i+1}$ is a simple group. Any two such decompositions of $ G$ have the same multiset of simple groups $ G_i/G_{i+1}$ up to ordering.

A filtration of $ G$ satisfying the properties above is called a Jordan-Hölder decomposition of $ G$.



"Jordan-Hölder decomposition theorem" is owned by djao.
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See Also: subnormal series

Also defines:  Jordan-Hölder decomposition

Attachments:
proof of the Jordan Hölder decomposition theorem (Proof) by djao
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Cross-references: properties, ordering, multiset, decompositions, simple group, quotient group, normal, filtration, finite group
There are 3 references to this entry.

This is version 5 of Jordan-Hölder decomposition theorem, born on 2002-01-05, modified 2004-06-23.
Object id is 1333, canonical name is JordanHolderDecompositionTheorem.
Accessed 4183 times total.

Classification:
AMS MSC: 20E32 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Simple groups)
Pending Errata and Addenda
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