Sylow Theorems/Examples/Sylow 2-Subgroups in Group of Order 32

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Example of Use of Sylow Theorems

The Sylow Theorems tell us nothing about the Sylow $2$-subgroups in a group of order $32$.


Proof

We have that $32 = 2^5$.

Hence the only Sylow $2$-subgroup in $G$ is $G$ itself.

$\blacksquare$


Sources