Timeline for Fixed point theorems
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 28, 2013 at 8:17 | comment | added | j.p. | Nice example. You can get the full Sylow theorem(s) from this fixed point theorem (not just the conjugacy), see mathoverflow.net/questions/18716/sylow-subgroups/19543#19543. | |
| Apr 11, 2013 at 8:33 | history | edited | Name | CC BY-SA 3.0 |
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| Apr 11, 2013 at 7:17 | history | edited | Name | CC BY-SA 3.0 |
added 23 characters in body
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| Apr 11, 2013 at 1:02 | comment | added | Qiaochu Yuan | This is false. For example, let $G = C_p \times C_q$. Then $G$ acts on a set of size $p$ and on a set of size $q$, hence on a set of size $p + q$. If $p, q > 1$ then this action doesn't have a fixed point, but we can arrange to have $\gcd(pq, p + q) = 1$ (e.g. take $p = 2, q = 3$). The correct statement is that $G$ needs to be a $p$-group. | |
| Apr 10, 2013 at 9:10 | history | answered | Name | CC BY-SA 3.0 |