query: Irreducibility of the standard representation of $S_n$.
positive_passages.docid: 41294
positive_passages.text: Permutation module of $S_n$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
negative_passages.docid: 65558
negative_passages.text: Irreducible in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 111935
negative_passages.text: Irreducible but not prime
negative_passages.docid: 31215
negative_passages.text: Irreducible cyclotomic polynomial
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 104349
negative_passages.text: Proof by induction involving symmetric groups
negative_passages.docid: 60816
negative_passages.text: Irreducibility of special cyclotomic polynomial.
negative_passages.docid: 120968
negative_passages.text: Isomorphism of stabilizer over $S_n$ to $S_{n-1}$
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 141792
negative_passages.text: Slick proof the determinant is an irreducible polynomial
negative_passages.docid: 137691
negative_passages.text: What are the self-normalizing subgroups of $S_n$?
negative_passages.docid: 64179
negative_passages.text: What is the difference between the standard representants of $\mathbb Z/q\mathbb Z$?
negative_passages.docid: 109440
negative_passages.text: How does $(12\dots n)$ and $(a\, b)$ generate $S_n$?
negative_passages.docid: 55432
negative_passages.text: Infinite distinct factorizations into irreducibles for an element
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 14139
negative_passages.text: $(12)$ and $(123\dots n)$ are generators of $S_n$