Timeline for Most harmful heuristic?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2017 at 5:23 | comment | added | Michael Cotton | This is a sad truth, really. Because in practice outside of pure algebra we almost never care about finite groups. In analysis and dynamics at least, the groups are almost always infinite and have natural topologies. Haha | |
| Jan 18, 2012 at 12:20 | comment | added | Chris Brav | Michael Artin's Algebra is a very good antidote to the typical finite-group-obsessed undergraduate algebra textbook. I used a lot of material from Artin's book when teaching group theory. I certainly found this more interesting, and I think the students did too. | |
| May 9, 2011 at 8:35 | comment | added | Jonathan Kiehlmann | I was tempted to try adding something like this to the false beliefs question. At a higher level, the same becomes true with the properties "finitely generated" or "residually finite". | |
| Mar 1, 2010 at 0:08 | comment | added | Pete L. Clark | @ML: right. I don't think textbooks can be fairly construed to be confusing about which results apply only to finite groups. BUT most undergraduate algebra textbooks I have seen certainly give the impression that finite groups are more important, more natural, and more studied than infinite groups, when many if not most mathematicians would say that the reverse is true. | |
| Oct 24, 2009 at 22:06 | comment | added | Michael Lugo | This got me in a lot of trouble in my first-year graduate algebra class. I also had a habit of forgetting that infinite groups even exist, which is the same sort of thing. | |
| Oct 24, 2009 at 21:54 | comment | added | S. Carnahan♦ | There are also profinite Sylow theorems, yielding the existence of a maximal pro-p subgroup. The proofs are relatively straightforward extensions of the finite proofs. | |
| Oct 24, 2009 at 21:47 | comment | added | Anton Geraschenko | By the way, the Sylow theorems make sense (and are true, I think) for infinite groups if you make a few modifications. A p-Sylow subgroup is a maximal subgroup which is a p-group. The first theorem (existence) is obvious by Zorn's lemma. The second (that all p-Sylows are conjugate) is interesting. The third is interesting if the index of a p-Sylow is finite or if the number of p-Sylows is finite. | |
| Oct 24, 2009 at 21:39 | history | answered | Gabe Cunningham | CC BY-SA 2.5 |