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?
*********************************************************
"the typical grad student"....where?? I studied in one of the most
reknowed graduate
schools in group theory around (Hebrew University in Jerusalem), and
the grad. student
there studies ONLY algebra as grad. subject, and the classical
undergraduate course in group theory. Less than one year all in all
from undergrad. to grad. in group theory...unless you aim to be a group
theory researcher, of course.
Topologists some times have tough times if they dismiss algebra and
then they want to mess up with algebraic topology. Perhaps this is what
happened to your friend.
As for "uninteresting spaces" with finite Pi_i or homology gps.: I
think some mathematicians would disagree with that...check for one
Poincare's Theorem.
Regards
Tonio

.

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