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- Any composition series for has length .
- The list of composition factors is the same for any two composition series. In other words, if form one composition series and form another, then for any simple group , the number of for which is isomorphic to equals the number of for which is isomorphic to .
- Jordan-Holder theorem for chief series: An analogous result, which states that any two chief series of a group have the same length and that the list of chief factors is the same.
- Finite composition length implies every subnormal series can be refined to a composition series
- Finite chief length implies every normal series can be refined to a chief series
- Jordan-Holder theorem for groups with operators
Some other related facts:
- Finite not implies composition factor-unique: There can exist finite groups for which there are different composition series with the composition factors occurring in different orders.
- Composition factor-unique not implies composition series-unique: Even if all composition series for a group have the same composition factors occurring in the same order, there may be more than one composition series.
- Finite not implies composition factor-permutable: There can exist finite groups for which not all possible orderings of the composition factors can be achieved using composition series.