Category:Definitions/Composition Series
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This category contains definitions related to Composition Series.
Related results can be found in Category:Composition Series.
Let $G$ be a finite group.
Definition 1
A composition series for $G$ is a normal series for $G$ which has no proper refinement.
Definition 2
A composition series for $G$ is a sequence of normal subgroups of $G$:
- $\set e = G_0 \lhd G_1 \lhd \cdots \lhd G_n = G$
where:
- $G_{i - 1} \lhd G_i$ denotes that $G_{i - 1}$ is a proper normal subgroup of $G_i$
such that:
- for all $i \in \set {1, 2, \ldots, n}$, $G_{i - 1}$ is a proper maximal normal subgroup of $G_i$.
Subcategories
This category has only the following subcategory.
S
- Definitions/Solvable Groups (3 P)
Pages in category "Definitions/Composition Series"
The following 9 pages are in this category, out of 9 total.