query: $[L:K]$ dividing $n!$ with $L=K(\alpha_1,...\alpha_n)$, and $L$ a splitting field of $f$ with $\alpha_1..\alpha_n$ zeros of $f$
positive_passages.docid: 133528
positive_passages.text: $\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
negative_passages.docid: 29545
negative_passages.text: $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
negative_passages.docid: 7324
negative_passages.text: Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$
negative_passages.docid: 45302
negative_passages.text: Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.
negative_passages.docid: 137858
negative_passages.text: Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
negative_passages.docid: 124685
negative_passages.text: How to show $(mn)!$ is divisible by $(m!)^n$?
negative_passages.docid: 133561
negative_passages.text: show that if $K$ is a field then $K[x]$ is principal
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
negative_passages.docid: 122530
negative_passages.text: Number of zeros at the end of $k!$
negative_passages.docid: 100162
negative_passages.text: Minimal polynomial over an extension field divides the minimal polynomial over the base field
negative_passages.docid: 66656
negative_passages.text: I have to find a splitting field of $x^{6}-3$ over $\mathbb{F}_{7}$
negative_passages.docid: 108914
negative_passages.text: Splitting field of $x^n-a$ contains all $n$ roots of unity
negative_passages.docid: 14918
negative_passages.text: Degree of splitting field of $X^n-1$ over some finite field
negative_passages.docid: 136770
negative_passages.text: Any field that contains the integers contains the rationals as a subfield (Analysis proof)
negative_passages.docid: 17604
negative_passages.text: What is a good asymptotic for $f_n = f_{n-1}+\ln(f_{n-1})$?
negative_passages.docid: 80144
negative_passages.text: Prove that $x-1$ divides $x^n-1$
negative_passages.docid: 85096
negative_passages.text: Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.