query: Prove that the group $\mathrm{GL}(n, \mathbb{Z})$ is finitely generated
positive_passages.docid: 154241
positive_passages.text: What is the easiest way to generate $\mathrm{GL}(n,\mathbb Z)$?
negative_passages.docid: 33945
negative_passages.text: Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
negative_passages.docid: 137739
negative_passages.text: Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
negative_passages.docid: 145112
negative_passages.text: Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
negative_passages.docid: 150007
negative_passages.text: Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$
negative_passages.docid: 43759
negative_passages.text: Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
negative_passages.docid: 94239
negative_passages.text: Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
negative_passages.docid: 130081
negative_passages.text: Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
negative_passages.docid: 146760
negative_passages.text: Prove that H is a subgroup of G
negative_passages.docid: 78580
negative_passages.text: Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
negative_passages.docid: 29269
negative_passages.text: fundamental group of $GL^{+}_n(\mathbb{R})$
negative_passages.docid: 110390
negative_passages.text: Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
negative_passages.docid: 131516
negative_passages.text: Subgroup generated by n-th powers of elements
negative_passages.docid: 59134
negative_passages.text: Proving idempotent elements in $\mathbb{Z}_n$
negative_passages.docid: 10816
negative_passages.text: Infinitely generated subgroup of a finitely one (weird)
negative_passages.docid: 13761
negative_passages.text: Automorphisms in $\mathbb{Z}_n$