/sci/ - Science & Math » Thread #11008884

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Group theory

Anonymous Fri 27 Sep 15:14:43 2019 No.11008884 View Reply Original Report

Quoted By: >>11008914 >>11008931 >>11008941 >>11009092 >>11010327 >>11010658 >>11013094 >>11013101 >>11013325 >>11013333

Let's have a thread for group theory
topic starter: your favorite group

Anonymous

Anonymous Fri 27 Sep 2019 15:29:08 No.11008914 Report

Quoted By:

>>11008884
E7 is nice
https://www.youtube.com/watch?v=IsnsUpwH_9Y

Anonymous

Anonymous Fri 27 Sep 2019 15:38:31 No.11008931 Report

Quoted By: >>11013024 >>11018381

>>11008884
What is group theory and why does /sci/ keep telling me to learn it despite not being at calc 1?

Anonymous

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Anonymous Fri 27 Sep 2019 15:40:36 No.11008941 Report

Quoted By: >>11009000 >>11009094 >>11017536

>>11008884
The abelian magma group Rock Paper Scissors is the best one

Anonymous

Anonymous Fri 27 Sep 2019 15:59:01 No.11008977 Report

Quoted By: >>11009026

0) a group (G,*) is a set G equipped with a binary operation * : GxG -> G, called the group action, that takes two members of G and maps them back onto G. In addition, * is
1) (a*b)*c = a*(b*c) Associative
2) a*b = b*a Commutative (optional)
3) a*id = a Existence of identity
4) a*(a^-1) = 1 Existence of inverse

Anonymous

Anonymous Fri 27 Sep 2019 16:08:32 No.11009000 Report

Quoted By: >>11009015 >>11009021

>>11008941
>The retard who "has a talent for finding patterns"
>Thinks rock paper scissors is a group without even defining an operation.
>Gets told it's not a group
>Gets told it's a magma
>AbeLIaN maGMa GrOuP
Get the fuck out of the gene pool, you absolute fucking retarded stupid fucking moronic cunt.

Anonymous

Anonymous Fri 27 Sep 2019 16:16:44 No.11009015 Report

Quoted By: >>11009016

>>11009000
In fairness, under the operation a * b = winner of the two (i.e., rock * paper = paper), it is a commutative magma.
https://en.wikipedia.org/wiki/Commutative_magma

Anonymous

Anonymous Fri 27 Sep 2019 16:17:05 No.11009016 Report

Quoted By: >>11009020

>>11009015
>magma
>group

Anonymous

Anonymous Fri 27 Sep 2019 16:18:54 No.11009020 Report

Quoted By: >>11009023

>>11009016
It's not a group, obviously. No identity, not associative. It does have divisibility though, so it's a commutative quasigroup.

Anonymous

Anonymous Fri 27 Sep 2019 16:19:30 No.11009021 Report

Quoted By: >>11009028

>>11009000
you're just jealous you didn't figure it out yourself. the smartest thing to do is always to rely on people who are smarter than yourself in areas you lack expertise. knowing where to find the information is always more valuable than having the information

see, no I taught you something, yet again proving my mental prowess

Anonymous

Anonymous Fri 27 Sep 2019 16:20:59 No.11009023 Report

Quoted By:

>>11009020
wait, i'm dumb,it's not divisible

Anonymous

Anonymous Fri 27 Sep 2019 16:21:48 No.11009026 Report

Quoted By: >>11009076

>>11008977
>Optional
>Definition

Anonymous

Anonymous Fri 27 Sep 2019 16:23:08 No.11009028 Report

Quoted By: >>11009031

>>11009021
What's the identity of RPS?

Anonymous

Anonymous Fri 27 Sep 2019 16:26:17 No.11009031 Report

Quoted By: >>11009035 >>11018385

>>11009028
Each element is their own identity. Minor hack, but it should work

Anonymous

Anonymous Fri 27 Sep 2019 16:27:51 No.11009035 Report

Quoted By:

>>11009031
An element being its own identity means it's idempotent. 0 is idempotent on multiplication, but it's not a multiplicative identity.

Anonymous

Anonymous Fri 27 Sep 2019 16:46:47 No.11009076 Report

Quoted By:

>>11009026
https://en.wikipedia.org/wiki/Abelian_group
https://en.wikipedia.org/wiki/Non-abelian_group

Anonymous

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Anonymous Fri 27 Sep 2019 16:52:47 No.11009092 Report

Quoted By: >>11011484 >>11011839

>>11008884
You should be able to solve this

Anonymous

Anonymous Fri 27 Sep 2019 16:53:27 No.11009094 Report

Quoted By:

>>11008941
Word you're looking for is commutative idempotent magma

Anonymous

Anonymous Fri 27 Sep 2019 18:46:33 No.11009414 Report

Quoted By: >>11013973

I heard the symmetry group of a circle is the orthogonal group O2. Why? How are they related?

Anonymous

Anonymous Fri 27 Sep 2019 23:01:38 No.11010327 Report

Quoted By: >>11010592

>>11008884
>favorite group
The Operation:
>On the set C, define AxB by (A-B)U(B-A), where - is the relative complement, and A and B are subsets of C
The Set:
>the empty set, lmao

Anonymous

Anonymous Sat 28 Sep 2019 00:10:17 No.11010592 Report

Quoted By: >>11011489

>>11010327
You can't have a group on the empty set because every group needs an identity element.
You can have a quasigroup or semigroup on the empty set though

Anonymous

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Anonymous Sat 28 Sep 2019 00:37:43 No.11010658 Report

Quoted By:

>>11008884
$\operatorname{Hom}(H_G(M^3,\mathbb{Z}_p),U(1))$

Anonymous

Anonymous Sat 28 Sep 2019 03:55:44 No.11011084 Report

Quoted By:

The group of permutations of infinite sequences of natural numbers, $S_{\infty}$ .

Anonymous

Anonymous Sat 28 Sep 2019 05:16:35 No.11011192 Report

Quoted By:

what is there to discuss about this topic in a casual setting

Anonymous

Anonymous Sat 28 Sep 2019 08:42:02 No.11011484 Report

Quoted By:

>>11009092
easy. use the classification of finite simple groups

Anonymous

Anonymous Sat 28 Sep 2019 08:43:50 No.11011489 Report

Quoted By:

>>11010592
what he described is a group on the power set of the empty set

Anonymous

Anonymous Sat 28 Sep 2019 12:42:00 No.11011839 Report

Quoted By:

>>11009092
Not op.
This is just sylow, right.
525 = 21x25, thus there exists a normal subgroup of order 25.

Anonymous

Anonymous Sat 28 Sep 2019 20:46:15 No.11012999 Report

Quoted By:

The free ring in one or maybe two variables.
Also, you can't go wrong with SU(2,C).

Anonymous

Anonymous Sat 28 Sep 2019 20:53:57 No.11013024 Report

Quoted By:

>>11008931
Because it has basically no prereqs; just go.

Anonymous

Anonymous Sat 28 Sep 2019 21:16:00 No.11013094 Report

Quoted By:

>>11008884
U(1)

Anonymous

Anonymous Sat 28 Sep 2019 21:18:32 No.11013101 Report

Quoted By: >>11020295

>>11008884
Associativity is for faggots, I'll much rather take a loop or even a quasigroup instead.

Anonymous

Anonymous Sat 28 Sep 2019 21:28:53 No.11013132 Report

Quoted By:

Monster group

Anonymous

Anonymous Sat 28 Sep 2019 22:21:59 No.11013325 Report

Quoted By:

>>11008884
A6

Anonymous

Anonymous Sat 28 Sep 2019 22:24:06 No.11013333 Report

Quoted By: >>11020266

>>11008884
I've been reading about the mapping class group of a surface, those are pretty interesting. For the sphere it's the trivial group, for the torus it's SL_2Z

Anonymous

Anonymous Sun 29 Sep 2019 01:06:33 No.11013973 Report

Quoted By:

>>11009414
O(2) consists of rotations and reflections (about the origin) of the Cartesian plane. you can do such things to a circle and it still looks as it did before.

Anonymous

Anonymous Sun 29 Sep 2019 02:00:09 No.11014686 Report

Quoted By:

Don't mind me, just a physishit passing by who loves him some $SU(2)$ and $SO(3)$ .

Anonymous

Anonymous Sun 29 Sep 2019 08:51:34 No.11016429 Report

Quoted By:

The four group obviously

Anonymous

Anonymous Sun 29 Sep 2019 18:09:53 No.11017536 Report

Quoted By:

>>11008941
ligma group

Anonymous

Anonymous Sun 29 Sep 2019 19:32:01 No.11017790 Report

Quoted By: >>11017967

Did you know that the statement "Every non-empty set has a group structure", is equivalent to the axiom of choice?

Anonymous

Anonymous Sun 29 Sep 2019 20:36:19 No.11017967 Report

Quoted By:

>>11017790
I finally grok the axiom of choice now. Thanks.

Anonymous

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Anonymous Sun 29 Sep 2019 23:29:44 No.11018373 Report

Quoted By:

take a look at that beaut', will yah

Anonymous

Anonymous Sun 29 Sep 2019 23:32:08 No.11018376 Report

Quoted By: >>11020211 >>11020356

O(1) is so advanced guys, the most advanced. Monster group fags BTFO

Anonymous

Anonymous Sun 29 Sep 2019 23:33:47 No.11018381 Report

Quoted By:

>>11008931
It's the study of certain sets equipped with certain binary operations. From an extremely short, simple definition that a grade schooler can understand comes a whole realm of beautiful and highly non-trivial structure.

Anonymous

Anonymous Sun 29 Sep 2019 23:36:08 No.11018385 Report

Quoted By:

>>11009031
yeah sorry each identity needs to be an identity for every other element

Anonymous

Anonymous Mon 30 Sep 2019 17:59:06 No.11020211 Report

Quoted By:

>>11018376
O(-1)

Anonymous

Anonymous Mon 30 Sep 2019 18:19:43 No.11020266 Report

Quoted By: >>11020292

>>11013333
what are you reading ?

Anonymous

Anonymous Mon 30 Sep 2019 18:29:59 No.11020292 Report

Quoted By:

>>11020266
Schultens introduction to 3 manifolds

Anonymous

Anonymous Mon 30 Sep 2019 18:30:07 No.11020295 Report

Quoted By:

>>11013101
based subCHADtion

Anonymous

Anonymous Mon 30 Sep 2019 18:49:03 No.11020356 Report

Quoted By:

>>11018376
wtf is this thing
https://en.wikipedia.org/wiki/Monster_group

Anonymous

Anonymous Mon 30 Sep 2019 19:29:17 No.11020437 Report

Quoted By:

>Choosing anything that isn't the Tits group

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