order, dividing


Subgroup formed by elements of order dividing n ★★

Author(s): Frobenius

\begin{conjecture}

Suppose $G$ is a finite group, and $n$ is a positive integer dividing $|G|$. Suppose that $G$ has exactly $n$ solutions to $x^{n} = 1$. Does it follow that these solutions form a subgroup of $G$?

\end{conjecture}

Keywords: order, dividing

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