Which groups are more better, commutative or noncommutative?

>>9097480
Commutative
>the (left) coset is...

>>9097480
This statement is correct and well known

Nonabelian obvsly

>>9097480
In terms of what?

>>9098441
Just overall. Which are more interesting, theorems and results about which are more important and interesting

>>9097480
Non-commutative. "Ching chong" and "chong ching" are not the same things.

>>9098446
Well permutation groups are arguably the most important groups, and all but the most trivial of them are noncommutative.

Commutative groups have a very nice characterization though.

>>9097770
Normal subgroups is where is at.

>>9097480
Non-commutative are better, they are more general.

Every commutative group can be a subgroup of a non-commutative group.

Is there any application of Non-Commutative Algebra in general? Just wondering...

>>9099397
but we got more insight into abelian groups, and because nonabelian groups are so general we know hardly anything about them

>>9098457
>Well permutation groups are arguably the most important groups
That's because all groups are permutation groups.

>>9098457
Sn is never completely commutative

Remember the only times permutations commute is when they disjoint

Retard

>>9099438
>are *subsets of* permutation groups
FTFY

>>9099430
>we know hardly anything about them
Sounds like an even better reason to study them.

Most of the easy math has been done.

I see more potential for novel results where most prior mathematicians chose to pursue results about 'convenient' structures.

Euclidean vs Non-Euclidean geometry is a notable example.

Try tying an arm behind your back and get new results.

TL;DR muh socks&shoes don't commute! (Walks barefoot)

AAAA WHY IS THERE ONLY ONE MENTION OF NORMAL GROUPS HERE, THEY ARE THE SHIT REEEE

>>9099471
>S2 is not commutative

>>9099618
it's not even a group

>>9099618
Looks like someone needs to retake undergrad algebra 1

>>9099618

So you're saying (12) (12) = (12) (12) ?

Nobody believes you

>>9099486
>are *subsets of* symmetric groups

>>9101015
should i kys?

>>9099415
you need non-abelian group theory for particle physics

>>9097480
Commutative groups are easy to work with and have many nice theorems and results (Pontryagin duality and the theory of locally compact abelian groups). Noncommutative groups are harder to deal with but are generally more interesting and have some unique structures (take lie groups for example)

Noncommutative noncocommutative quantum groups are bettererest.