Re: Why are finite groups so much of math curriculum?

adomplayer@xxxxxxxxx wrote:
Hi Please dont take this as me ranting, I was actually trying to argue
in FAVOR of finite groups, when a friend of mine suggested they are
kind of a waste of time. To my chagrin, I realized I had great
difficulty coming up with examples of places finite group theory is
useful. My first suggestion was topology but my friend pointed out
correctly that finite groups are quite rare there in practice and any
space whose pi_1 or pi_n or H_n groups are finite is almost by
definition uninteresting. I have to admit he kind of has a point: the
typical grad student will spend 2 or 3 years studying finite group
theory and for what? My friend did acknowledge they are a little
useful in Galois theory since they let us understand which intermediate
fields lie between two given fields, but then this particular
application can mostly be done with computers now and certainly doesn't
take 2 to 3 years to comprehend..


I have to take exception to the claim

... any space whose pi_1 or pi_n or H_n groups are
finite is almost by definition uninteresting.


One might point out that the Poincaré homology sphere is relatively
interesting, even historically interesting, and that the classifying
space for the infinite orthogonal group is a relatively important
object, seeing as how that's where several families of characteristic
classes live.

As for the claim

... the typical grad student will spend
2 or 3 years studying finite group theory ...

I find it hard to believe. Mind you, it has been more than a few
years (it's going on 30) since I was in graduate school, but can
things have changed that much? In my day, it was only the students
who were concentrating in group theory who studied finite groups
for that length of time. Now, it could have been that we had more
pressing needs, such as fighting off dinosaurs and rubbing sticks
together to produce that hot orange stuff we used for that new-
fangled "cooking" technology, but I kinda doubt it.

Dale
.

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  • Why are finite groups so much of math curriculum?
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