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Image of the reduction of a maximal order in a central simple algebra over $\mathbb Q$
Suppose $A$ is a $n^2$-dimensional central simple algebra over $\mathbb Q$, and $O_A$ is an maximal order of $A$.
Choose a finite place $p$ such that $A \otimes \mathbb Q_p \cong M_n(\mathbb Q_p)$. ...