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