Timeline for Categorical proof subgroups of free groups are free?
Current License: CC BY-SA 3.0
13 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 1, 2015 at 15:05 | vote | accept | Exterior | ||
| Jan 29, 2015 at 17:22 | comment | added | Qiaochu Yuan | @Todd: Oh, so a number theorist! | |
| Jan 29, 2015 at 1:43 | comment | added | Todd Trimble | @DavidRoberts Your remark reminds me of an anecdote about the movie, "It's My Turn", starring Jill Clayburgh as a math professor (famous in math circles for her proof of the snake lemma). At one point in the movie her father introduces her as someone who works in the area of finite simple groups. But apparently that scene had to be edited. The father had first introduced his daughter as someone working in the area of finite, simple, abelian groups. A mathematician present during the screening broke out in laughter on hearing this. Source: world.std.com/~reinhold/mathmovies.html#Gagola | |
| Jan 28, 2015 at 15:43 | comment | added | Jeremy Brazas | In the topological group category, a subgroup of a free topological group need not be a free topological group (though there is a positive answer when the subgroup is assumed to be open). | |
| Jan 28, 2015 at 12:06 | history | edited | Ibrahim Tencer | CC BY-SA 3.0 |
minor clarification - <2, 3> is free in (N, *)
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| Jan 28, 2015 at 10:51 | comment | added | YCor | It's not free in the categorical sense, but for the free $K$-fields $K(x_1,\dots,x_n)$, discussing whether its $K$-subfields are free amounts to the question whether unirational implies rational. For instance for $K=\mathbf{C}$, the answer is yes for small $n$ (at least $n\ge 2$) but not for large $n$. | |
| Jan 28, 2015 at 1:48 | comment | added | Tom Church | That subalgebras of free Lie algebras over a field are free was proved by Shirshov and Witt independently, in Shirshov, Podalgebry svobodnykh lievykh algebr (Russian: Subalgebras of free Lie algebras), Mat. Sbornik N.S. 33(75) (1953), 441–452, and Witt, Die Unterringe der freien Lieschen Ringe (German: Subrings of free Lie rings), Math. Z. 64 (1956), 195–216. The same result was proved for free restricted Lie algebras in characteristic $p$ by Bryant-Kovács-Stöhr in Subalgebras of free restricted Lie algebras, Bull. Austral. Math. Soc. 72 (2005), no. 1, 147–156 (repairing earlier proofs). | |
| Jan 28, 2015 at 1:12 | comment | added | Todd Trimble | @DavidRoberts Yes, I know. But it's nevertheless a good example for those who haven't thought much about projective modules. | |
| Jan 28, 2015 at 1:03 | comment | added | Arturo Magidin | It's not even true that subobjects of relatively free groups are relatively free groups (in the corresponding variety). In fact the only Schreier varieties of groups are the variety of all groups, all abelian groups, and of all abelian groups of exponent $p$ ($p$ a prime). | |
| Jan 28, 2015 at 1:00 | comment | added | David Roberts♦ | "some vector bundles are not trivial bundles." ho ho ho - this made me laugh. A bit like saying there are some finite simple groups that are nonabelian... | |
| S Jan 27, 2015 at 23:50 | history | answered | Todd Trimble | CC BY-SA 3.0 | |
| S Jan 27, 2015 at 23:50 | history | made wiki | Post Made Community Wiki by Todd Trimble |