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 Apr 26 answered Why is $\mathbb F_5(\root{15}\of t)$ not normal over $\mathbb F_5(t)$? Apr 10 asked On the restriction of field homomorphisms to subfields Jan 19 reviewed No Action Needed How to calculate the correlation between two ratings Jan 5 comment Which of the following field properties are correct? One way would be to use that $x^4-x^3+x^2-x+1=\Phi_5(-x)$, and that $\Phi_5(x)$ is irreducible. Dec 14 comment Showing that $|\text{Hom}_\mathbb{Q}(K,K)|=6$ Consider complex conjugation as a $\Bbb{Q}$-automorphism of $L$. Also, note that $\Bbb{Q}(\alpha,\beta,\bar{\beta})=\Bbb{Q}(\alpha,\beta)$, which can save you some writing. Dec 14 comment How do I find a splitting field $x^8-3$ over $\mathbb{Q}$? It is not enough that $\zeta\notin\mathbb{Q}(\sqrt[8]{3})$ for $K$ to be of dimension $4\cdot8=32$ over $\mathbb{Q}$. For example, the splitting field of $x^8-2$ over $\Bbb{Q}$ has degree $16$ even though $\zeta\notin\mathbb{Q}(\sqrt[8]{2})$. Dec 14 revised Degree of splitting field for $x^3-3x-1$ over $\Bbb Q$ and $\Bbb F_5$ added 86 characters in body Dec 14 answered Degree of splitting field for $x^3-3x-1$ over $\Bbb Q$ and $\Bbb F_5$ Nov 29 answered What is the splitting field of $(X^3-2)(X^3-3)(X^2-2)$ Nov 29 answered A galois extension being the splitting field of $X^p-a^p$. Nov 20 comment Proving 2047 is not an euler pseudoprime It's a Jacobi symbol. Nov 14 comment Subgroups of $S_n$ There's also an element of order $10$. Nov 14 comment Subgroups of $S_n$ If $n\geq 3+4+5=12$, $S_n$ contains a cyclic subgroup of order $60$: take the subgroup generated by an element of cycle type $(3,4,5)$. If $n<12$, $S_n$ has no cyclic subgroup of order $60$, since no element of $S_n$ has order $60$. Nov 8 answered Proof Verification Regarding Image of $K$-homomorphisms of a Normal Extension Nov 8 answered Find root of polynomial over finite field Jun 15 awarded Popular Question Jun 4 reviewed No Action Needed What is the probability a shuffled deck of cards will have no number-wise repetitions? Jun 1 reviewed No Action Needed Continuously extending a set of independent vectors to a basis. Jun 1 reviewed No Action Needed Definition of functions in $L^p$ space Jun 1 reviewed No Action Needed Complement of the radical of a bilinear form