Definition:Refinement of Normal Series/Proper Refinement
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Definition
A proper refinement of a normal series is a refinement which is not equal to the original normal series.
That is, it contains extra (normal) subgroups which are not present in the original normal series.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 71$