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 Feb 13 comment Evaluation of $\int_{0}^{a}\sin^{-1} \sqrt \frac{x}{a-x} dx$ Use a limit of a/2 Dec 27 comment Automorphisms of the rational function field , and fractional linear transformation An automorphism $\phi$ must send t to a rational function in $t$ and $\phi$ must be invertible. Dec 19 comment Conjugacy classes in a group of order $p^aq^b$ @M.R. You are correct: either the three orders are $p,q,pq$ or $p,p^2,q$. Dec 18 comment Conjugacy classes in a group of order $p^aq^b$ @M.R. If there is an element $a$ of order say $p^xq^y$ then $b=a^{p^x}$ has order $q^y$. Dec 17 comment Conjugacy classes in a group of order $p^aq^b$ In ii) the only possible orders are $p, q, pq$ The first two because of the Sylow theorems and the third case follows from this. Thus the Sylow subgroups are elementary abelian isomorphic to $Z_p^a$, $Z_q^b$. Aug 27 comment On the number of group homomorphisms from $S_n$ to $S_m$ In $S_m$ we can look at the subgroup fixing $m$ and then we get the subgroup $S_{m-1}$. Aug 23 comment Finding Galois group of $K=\Bbb{Q}(\omega,\sqrt2)$, showing that $K=\Bbb{Q}(\omega\sqrt2)$, and finding $\operatorname{min}(\omega\sqrt2,\Bbb{Q})$ $a=\omega\sqrt{2}$ then $a^2=2\omega^2$, hence $b=\omega^2\in K$ so also $b^2=\omega \in K$. Jul 27 comment Determine the galois group of $x^5+sx^3+t$ If $s=15, t=81$ then the group is $D_5$. Jul 27 comment Determine the galois group of $x^5+sx^3+t$ If $s=0$ then the Galois group is not $S_5$. Jul 27 comment Determine the galois group of $x^5+sx^3+t$ It is not always $S_5$. For $s=10, t=\pm 5$ the group is $F_{20}$. Jul 19 comment Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$ @TheSubstitute We want $a+b$ or $a-b$ so by squaring we can evaluate the algebra. Jul 18 comment Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$ For example an invariant under $g$, is the element $a+b=\sqrt{7}$. (You can easily compute a^2+b^2+2ab). Jul 18 comment computing the galois group of a polynomial @TheSubstitute Thanks, I made revisions. Jul 17 comment The Galois group of a specific polynomial $f(x) = x^6-2x^3+2 \in Q[x]$ Let $w$ be a primitve cube root of 1. The splitting field is $Q(i, w, (1+i)^{1/3})$ which has degree 12. Jun 17 comment Q-automorphisms determind by associates to id-element? It is true that the automorphism maps an element r to another root of the minimal polynomial of r over Q. May 29 comment Prove that $\sin(a)$ + $\cos(a)\leq\sqrt{2}$ It looks like you want to show $|\sin(a)+\cos(a)|\le \sqrt{2}$. Jan 8 comment Kernel and image of a homomorphism $SL(2,5)\to S_5$ $S_5$ has a trivial center. Aug 8 comment Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group Aug 7 comment How prove $-\sqrt{2}\log(\cos x)\leq\sqrt{x\tan x-\sin^{2}x}$? Use the derivative Aug 6 comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$ @JyrkiLahtonen That is not correct. For example the conjugates of $\sqrt{2}$ over the rationals are distinct but not linearly independent.