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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
possible duplicate of $K$ is a normal subgroup of a finite group $G$ and $S$ is a Sylow $p$-subgroup of $G$. Prove that $K \cap S$ is a Sylow $p$-subgroup of $K$.
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.
Aug
6
comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$
@PraphullaKoushik I should have said $1, s, \cdots, s^5$ are independent.