query: For q a power of an odd prime p, find a 2-Sylow subgroup of $GL_{2}(F_{q})$
positive_passages.docid: 142938
positive_passages.text: Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
negative_passages.docid: 37093
negative_passages.text: If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
negative_passages.docid: 115427
negative_passages.text: Galois group of $\prod_{i=1}^{p-1} (X^2-i)$
negative_passages.docid: 11957
negative_passages.text: G is the product of its Sylow subgroups
negative_passages.docid: 157496
negative_passages.text: Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
negative_passages.docid: 109286
negative_passages.text: Galois group of $x^4-2x^2-2$
negative_passages.docid: 126893
negative_passages.text: A group of order 2p (p prime) and other conditions - prove abelian.
negative_passages.docid: 64408
negative_passages.text: Subgroup of $\mathbb{Q}$ with finite index
negative_passages.docid: 90449
negative_passages.text: Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
negative_passages.docid: 143314
negative_passages.text: Sylow subgroup of $S_{p^2}$
negative_passages.docid: 117744
negative_passages.text: $p$-Sylow in quotient groups
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 100439
negative_passages.text: Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$
negative_passages.docid: 117789
negative_passages.text: Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
negative_passages.docid: 37677
negative_passages.text: Radical of $\mathfrak{gl}_n$
negative_passages.docid: 38153
negative_passages.text: Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .