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Feb
25
comment Complex numbers subgroup
He’s writing the powers of $i$ in order: $i^0$, $i^1$, $i^2$, $i^3$. But it doesn’t matter.
Feb
24
comment n-by-n degree grid on a sphere?
There are no spherical rectangles, ’cause the four angles of a quadrilateral have to add up to more than $360^\circ$. And don’t forget: the “parallels” of latitude are not “straight”, i.e. not geodesics, the way the lines of longitude are. They’re what are known as “small circles” on the surface of the sphere.
Feb
24
answered Prove $x^5-2$ is irreducible over $\mathbb{Z}_{31}$
Feb
23
comment How to find a p-adic expansion?
This is the way I like to look at it. For basic $p$-adic computations, what you learned by fifth grade should suffice.
Feb
23
answered Showing that a given field is the splitting field of a given polynomial
Feb
21
comment Does $\lim_{x \to 0} \frac{\sin (\left \lfloor x \right \rfloor)}{\left \lfloor x \right \rfloor}$ exist?
@mathmandan, again I’ve read only part way through. Thanks.
Feb
20
answered Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
Feb
20
comment Any advantage when proving linear algebra statements without using bases?
But sometimes a basis-free argument is more illuminating.
Feb
19
comment Partial fractions problem
Sorry, what is the question?
Feb
19
comment Automorphism group of the general affine group of the affine line over a finite field?
Ah, that’s good. This looks more like the situation with collineations of the (desarguesian) projective plane. Thank you.
Feb
19
comment Automorphism group of the general affine group of the affine line over a finite field?
To me, $AGL(k)$ means those coming from identity on $k$ (!) Gotta go. e-mail me if you like.
Feb
19
comment Automorphism group of the general affine group of the affine line over a finite field?
Why not? Do you have an example of an unextendable one?
Feb
19
comment Automorphism group of the general affine group of the affine line over a finite field?
Then before all else, you have to decide on what the automorphism group of $k^+$ is. It’s a finite vector space over the prime field $\Bbb F_p$, so you’re talking about a general linear group over the prime field. These are well understood…
Feb
19
comment Automorphism group of the general affine group of the affine line over a finite field?
Most folks would assume that you wanted to consider only those maps that come from the identity automorphism of $k$. Are you sure you want that full generality?
Feb
19
comment What does $E^{2}$ mean in this context?
$E\,$ for “Euclidean”.
Feb
18
comment Why are the rules of logic universally applicable?
What is “$2$” ?
Feb
18
comment Why is the inverse of a sum of matrices not the sum of their inverses?
When people ask “Why isn’t (such-and-such) true?” I like to answer: In mathematics, nothing is true, unless you have a proof for it.
Feb
18
comment Information about the cyclic group $C_{p^n}$, where $p$ is prime and $n\geq 2$
I suppose I should have said as well that every extension of finite fields is cyclic, so that you can get the particular cyclic Galois groups you were wondering about from such extensions. And that the general question of which abelian Galois groups occur for extensions of general number fields is covered by Class Field Theory. And that there isa Local Class Field Theory describing the abelian extensions of local fields like the $p$-adic numbers and their finite extensions.
Feb
18
answered Information about the cyclic group $C_{p^n}$, where $p$ is prime and $n\geq 2$
Feb
17
comment Argument of $3+4i$
Maybe it was my error, @Ozera, to interject number theory into a question that almost surely arose in a complex-variable context.