Composition Series/Examples/Cyclic Group C8
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Example of Composition Series
There is $1$ composition series of the cyclic group $C_8$, up to isomorphism:
- $\set e \lhd C_2 \lhd C_4 \lhd C_8$
Proof
From Cyclic Group is Abelian and Subgroup of Abelian Group is Normal, all subgroups of $C_n$ are normal in $C_n$.
This leads directly to the composition series:
- $\set e \lhd C_2 \lhd C_4 \lhd C_8$
$\blacksquare$
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 74 \ \beta$