query: Find the orders of $M_3(\mathbb Z_2)$ and $GL_3(\mathbb Z_2)$
positive_passages.docid: 55719
positive_passages.text: Order of general- and special linear groups over finite fields.
negative_passages.docid: 118310
negative_passages.text: How to find $\operatorname{Gal}(S/\mathbb{Q})$
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 137201
negative_passages.text: Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
negative_passages.docid: 30404
negative_passages.text: Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
negative_passages.docid: 118898
negative_passages.text: Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
negative_passages.docid: 12110
negative_passages.text: How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
negative_passages.docid: 106577
negative_passages.text: If G is not abelian with order $p^3$ then $G'=Z(G)$
negative_passages.docid: 36137
negative_passages.text: Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
negative_passages.docid: 42213
negative_passages.text: Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
negative_passages.docid: 111814
negative_passages.text: Precise connection between complexification of $\mathfrak{su}(2)$, $\mathfrak{so}(1,3)$ and $\mathfrak{sl}(2, \mathbb{C})$
negative_passages.docid: 110390
negative_passages.text: Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 73713
negative_passages.text: Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
negative_passages.docid: 56420
negative_passages.text: Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
negative_passages.docid: 94296
negative_passages.text: Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$