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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.
Jul
31
comment Characterization of solvable groups in terms of subgroups of certain orders?
en.wikipedia.org/wiki/Hall_subgroup
Jul
31
comment Incentre and excentre of a triangle
what does equivalent mean?
Jul
31
comment Largest Equilateral Triangle in a Polygon
It is not in Math Reviews either. Can you post a pdf?
Jul
30
comment Groups of order $n^2$ that have no subgroup of order $n$
Must $n$ be even?
Jul
30
comment Largest Equilateral Triangle in a Polygon
@NovaDenizen Thanks, so maybe make centroid of the triangle as far as possible from the vertices and inside the polygon.
Jul
30
comment Canonical embedding into dual space?
What if it is an inner product space?
Jul
29
comment Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
How many Sylow p-subgroups?Sylow q-subgroups?
Jul
28
comment Finitely generated submodules
use Smith Canonical form
Jul
26
comment Another Presentation of Certain Cyclic Groups
Thanks for answering the other case too.
Jul
26
comment Another Presentation of Certain Cyclic Groups
@B.S.That follows from "abelianizing" the presentation (for both cases).