/sci/ - Science & Math » Thread #14034036

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The monster group

Anonymous Thu 30 Dec 17:40:53 2021 No.14034036 View Reply Original Report

Quoted By: >>14034277 >>14034589 >>14036192 >>14038099 >>14040731

What the fuck is it?

Anonymous

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Anonymous Thu 30 Dec 2021 18:13:58 No.14034199 Report

Quoted By: >>14038215

A simple group is one which has no normal subgroups other than itself and the group of just the identity. To explain the monster it would help to have some background on finite simple groups in general.

Anonymous

Anonymous Thu 30 Dec 2021 18:23:32 No.14034240 Report

Quoted By: >>14034403 >>14034410 >>14034439 >>14034519 >>14036213

does this bullshit even have real life applications?

Anonymous

Anonymous Thu 30 Dec 2021 18:30:36 No.14034277 Report

Quoted By:

>>14034036
Mathematicians shouldn't be so cute with their naming

Anonymous

Anonymous Thu 30 Dec 2021 18:53:59 No.14034403 Report

Quoted By: >>14036222

>>14034240
I think mathematicians are trying to classify all possible fundamental groups. Fundamental as in atoms in chemistry and elementary particles in physics, with any other group built as some combination of these basic groups. That can have an application to physics.

Anonymous

Anonymous Thu 30 Dec 2021 18:55:18 No.14034410 Report

Quoted By:

>>14034240
Something something string theory

Anonymous

Anonymous Thu 30 Dec 2021 19:01:31 No.14034439 Report

Quoted By:

>>14034240
Look up "monstrous moonshine". The monster group is related to the j-invariant, which as far as I can tell is some bullshit used in number theory and complex manifolds.

Anonymous

Anonymous Thu 30 Dec 2021 19:20:26 No.14034519 Report

Quoted By:

>>14034240
yes, specifically in physical chemistry

Anonymous

Anonymous Thu 30 Dec 2021 19:34:06 No.14034589 Report

Quoted By: >>14036227 >>14038120 >>14040705

>>14034036
i am probably just speaking from ignorance, but the whole classification of finite simple groups always seemed like pure autism to me, on the level of set theory and related fields.
i dont think i ever met anyone that was interested in these topics.

Anonymous

Anonymous Fri 31 Dec 2021 01:19:26 No.14036192 Report

Quoted By:

>>14034036
bump

Anonymous

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Anonymous Fri 31 Dec 2021 01:25:13 No.14036213 Report

Quoted By:

>>14034240
Of course

Anonymous

Anonymous Fri 31 Dec 2021 01:28:51 No.14036222 Report

Quoted By:

>>14034403
They're called simple groups, fundamental group means something else in math. All finite simple groups have been classified. It was one of the major achievements of 20th century mathematics. The infinite ones many never be completely classified due to the complexity of the task.

Anonymous

Anonymous Fri 31 Dec 2021 01:31:04 No.14036227 Report

Quoted By:

>>14034589
The classification is used to prove a lot of theorems about finite groups by reducing them to special cases. Few people under the age of 70 are likely to know the proof of the classification in any detail though. It's tens of thousands of pages long.

Anonymous

Anonymous Fri 31 Dec 2021 14:37:39 No.14038099 Report

Quoted By:

>>14034036
I have never heard this described in the context of numbers.

Anonymous

Anonymous Fri 31 Dec 2021 14:43:38 No.14038120 Report

Quoted By:

>>14034589
Maybe it's just like filtering and putting books in the right directories and classifying everything for usefulness?

Like collecting information about species

Anonymous

Anonymous Fri 31 Dec 2021 15:13:38 No.14038215 Report

Quoted By:

>>14034199
woah i had no idea you could attach pdfs

Anonymous

Anonymous Sat 01 Jan 2022 01:53:10 No.14040705 Report

Quoted By: >>14040714

>>14034589
Set theory is very interesting though

Anonymous

Anonymous Sat 01 Jan 2022 01:55:04 No.14040714 Report

Quoted By: >>14040982

>>14040705
*Vomits*

Anonymous

Anonymous Sat 01 Jan 2022 01:57:57 No.14040731 Report

Quoted By: >>14041019 >>14041202

>>14034036
A huge sporadic group containing most (but not all) other sporadic groups, with a ton of weird connections to disparate fields of math

Anonymous

Anonymous Sat 01 Jan 2022 03:01:00 No.14040982 Report

Quoted By:

>>14040714
Read stuff from the Cabal

Anonymous

Anonymous Sat 01 Jan 2022 03:13:22 No.14041019 Report

Quoted By: >>14041185

>>14040731
Do sporadic groups just contain specific numbers/elements and encompass a sort of relationship between them?

Anonymous

Anonymous Sat 01 Jan 2022 04:01:14 No.14041185 Report

Quoted By: >>14041202

>>14041019
Sort of. Think of them like lists of group actions applicable to the same structure. The lists provided by the "happy family" are all applicable to the monster.

Anonymous

Anonymous Sat 01 Jan 2022 04:07:21 No.14041202 Report

Quoted By: >>14041226

>>14040731
>>14041185
What do these sporadic groups describe anyways? Like I know the other basic groups describe shit like rotating a cube on it's axis or reflecting a pentagon or whatever. So what actions happen to what geometric objects in the sporadic groups?

Anonymous

Anonymous Sat 01 Jan 2022 04:13:42 No.14041226 Report

Quoted By:

>>14041202
The objects themselves are abstract and require far too many dimensions for us to meaningfully imagine outside of matrix expressions and the like. The actions are the same.

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