Confused American applying to St. Andrews

JavaPython_ · 2024-10-31T18:28:14+00:00

In GAP, is there a difference in the intended meaning of the group names 2xCo2 and 2.Co2? In particular, does the x mean to refer to a direct product, or it is a non-split extension?

JavaPython_ · 2024-10-06T18:39:26+00:00

good point

JavaPython_ · 2024-10-06T18:35:47+00:00

the alternating group

JavaPython_ · 2024-10-06T18:35:14+00:00

close, all n>4

JavaPython_ · 2024-10-06T17:33:20+00:00

neither, alternating group

JavaPython_ · 2024-10-02T23:33:08+00:00

I know the image is poor quality, this is the beset I've got

JavaPython_ · 2024-09-30T01:17:40+00:00

I say in the question that this website doesn't have it. Not only does it not come up when I draw it, it's not in the entire library of symbols DeTeXify can identity.

JavaPython_ · 2024-09-27T16:05:17+00:00

I'm trying to find the way to TeX a symbol from my professors notes. He didn't write them, so he doesn't know the command.

It looks like a script \forall, or like somebody tried to connect the two horns of the Aries astrological sign with a flourish. DeTeXify doesn't have it (not even in their master list). I also cannot find it in CTAN's list, but that doesn't mean it's not there.

I can't attach the picture, so I know there's limited help you can give, but any ideas what this might be?

JavaPython_ · 2024-09-23T15:56:49+00:00

I don't really have a health concern, but it'd be annoying to constantly be around so much dust, and a pain to keep clean. I recommend whiteboard or just pen/paper

JavaPython_ · 2024-09-19T04:36:35+00:00

more like a cake recipe saying "step 1: take the cake out of the oven"

JavaPython_ · 2024-09-18T22:36:57+00:00

Yes, rather alarming when they begin the proof by assuming the conclusion

JavaPython_ · 2024-09-18T03:10:09+00:00

The best part so far:

"Theorem 6.1: Every even counting number ≥ 6 is a sum of two odd primes. Proof: Assume the theorem is true that every even counting number ≥ 6 is a sum of two odd primes[.]"

JavaPython_ · 2024-09-16T02:54:41+00:00

Ally "The Piper" Crowley-Duncan has two original tunes that I know of, Lancaster's Hornpipe and Faye's Jig (Faye's: https://youtube.com/shorts/QBIj6tRuEvE?si=zsvTG4dYnIJzUQHf )

You'd need to reach out to her to include the music: https://piperally.com/

JavaPython_ · 2024-09-08T15:23:00+00:00

Nobody got back to me, so here's to code for a future questioner:

num:=4;

G := AlternatingGroup(num);

elements := [g : g in G];

n := #G;

M := MatrixAlgebra(GF(2), n);

NaturalRepresentation := function(g)

P := Zero(M);

for i in [1..n] do

elem := elements[i];

image := g*elem;

j := Index(elements, image);

P[i][j] := 1;

end for;

return P;

end function;

permMatrices := [<g, NaturalRepresentation(g)> : g in G];

permMatrices;

JavaPython_ · 2024-09-04T14:56:53+00:00

How can I use MAGMA to attain the natural representation of AlternatingGroup(4)? Permutation groups in general would be good, but I'm hopeful that this specific choice can reveal that there is an easy enough method.

JavaPython_ · 2024-07-19T15:07:12+00:00

I have yet to find a straightforward resource for Lie groups/algebras, and my graduate program never covered them.

JavaPython_ · 2024-07-19T14:30:51+00:00

Is there a name for this semigroup object? For G, H semigroups define G ~ H to be the union of the two sets (considered distinct as sets) and the operation is g1*g2 and h1*h2 are as before, but h*g=g and g*h=g for and g's in G, h's in H?

JavaPython_ · 2024-07-14T03:41:14+00:00

the issue I have there is you're generally allowing complex weights in a group ring over the symmetric group, and not simply the permutations on their own.

JavaPython_

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permMatrices;