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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 $Z_p^a$, $Z_q^b$.
Nov
28
reviewed Approve Draw phase portrait of this system
Nov
15
reviewed Approve Convergence of series $\sum\limits_{k=1}^\infty\frac{1}{X_1+\dots+X_k}$ with $(X_k)$ i.i.d. non integrable
Sep
28
reviewed Approve Statistical property proof
Sep
13
answered Galois group of $X^3-10$ over $\mathbb{Q} (i\sqrt{3})$
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 $b^2=\omega \in K$.
Aug
18
answered Normal extension of $\mathbb{Q}(1-2i\sqrt2)/\mathbb{Q}$
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
answered Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$
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
18
revised computing the galois group of a polynomial
deleted 123 characters in body