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
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $11$: The Sylow Theorems: Exercise $1 \ \text{(c)}$