Reputation
3,124
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 6 18
Newest
 Yearling
Impact
~97k people reached

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.
Aug
6
comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$
@PraphullaKoushik You can easily check that for $u=s+s^5$ then 1, u, u^2, u^3 are linearly independent over the rationals (using that $1, s, s^2, s^3, s^4, s^5, s^6$ are linearly independent over $Q$). Thus $u$ can't satisfy a rational polynomial of degree at most 3. It then follows easily that the degree 6 polynomial is irreducible.
Aug
6
comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$
@Praphulla Your polynomial is irreducible over $Q(\sqrt{-7})$ so multiply by its complex conjugate to get an irreducible polynomial over $Q$
Aug
6
comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$
Multiply your cubic by its complex conjugate. Your cubic is $x^3+x^2+ \frac{1}{2}(3+\sqrt{7}I)x-1$
Aug
1
comment Unique normal subgroups of every possible order
@WilliamStagner That's proven in 39941.
Aug
1
comment Do two points determine a unique line in 4D space?
@8bar If the two points are v, w then the plane has exactly the points $sv+tw$ for scalars $s,t$. You could find two vectors perpendicular to this plane and thereby determine this plane as the intersection of two 3-dimensional hyperplanes.
Jul
31
comment Groups of order $n^2$ that have no subgroup of order $n$
I checked n=31...44; all such groups have a subgroup of index n.