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D1nk0
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08 May 2008, 12:51 am

Groups, the subject of Group Theory...arent they great or what! 8)
The abelian ones are too simply for my tastes though, I like Non-Abelian groups.
But lemme tell you, without commutativity those non-abelian groups are SO much more tedious to
compute(with)! 8O



nontrivial
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08 May 2008, 1:01 am

If you love groups, you'd love my job. My job is to study Coxeter groups (and some of their cousins, e.g. Artin groups).

Non-abelian groups can be a pain, but I think they're also the real reason why we invented groups in the first place - to deal with things like permutations and functions that simply don't commute. If all we ever dealt with was abelian groups, we probably wouldn't have come up with beautiful ideas like the Sylow theorems, and we certainly wouldn't be able to talk about groups acting on geometric cell complexes (which is my personal meal ticket :) ).



D1nk0
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08 May 2008, 11:30 am

nontrivial wrote:
If you love groups, you'd love my job. My job is to study Coxeter groups (and some of their cousins, e.g. Artin groups).

Non-abelian groups can be a pain, but I think they're also the real reason why we invented groups in the first place - to deal with things like permutations and functions that simply don't commute. If all we ever dealt with was abelian groups, we probably wouldn't have come up with beautiful ideas like the Sylow theorems, and we certainly wouldn't be able to talk about groups acting on geometric cell complexes (which is my personal meal ticket :) ).


What is your Job, eh? I personally am fond of Lie Groups which are continuous.



twoshots
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08 May 2008, 5:01 pm

I've pretty much forgot everything I learned about groups last fall over the course of this semester. I have no occasions to actually make use of them. :'(



nontrivial
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08 May 2008, 6:49 pm

I'm a graduate student, working on my dissertation.

Lie groups are nice as well, but I don't know nearly as much about them as I should.



D1nk0
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08 May 2008, 8:49 pm

nontrivial wrote:
I'm a graduate student, working on my dissertation.

Lie groups are nice as well, but I don't know nearly as much about them as I should.


What piqued my curiosity about Lie Groups recently was their role in the Banach-Tarski Paradox. Im a graduate student in Math seeking to pursue Set Theory.