Given a group $G$ with order $28 = 2^2 \cdot 7$. Sylow-Theory implies that there is a exactly one $7$-Sylow-Subgroup of order $7$ in $G$, and $1$ or $7$; $2$-Sylow-Subgroups.
Where to go from here concerning the number of elements of order $7$?
If $x$ is an element of order $7$ then the subgroup $\langle x\rangle$ generated by $x$ has order $7$...
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3 years ago