Timeline for Awfully sophisticated proof for simple facts
Current License: CC BY-SA 3.0
2 events
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| Aug 2 at 2:45 | comment | added | Noah Schweber | Although there is content here: we have on the one hand a family of $6\cdot 5\cdot 4$ "obvious" embeddings (injections from $\{1,2,3\}$ to $\{1,2,3,4,5,6\}$, and a further $6!$-many "Cayleyized" embeddings (bijections from $S_3$ to $\{1,2,3,4,5,6\}$). So if we care about how $S_3$ can be a subgroup of $S_6$, there's additional variety being provided. (I've used essentially this (I think 5/120 in my case?) as an example of how "amorphous" abstract groups can be and how many truly different ways one group might be embeddable into another, although I don't know how compelling it was.) | |
| Feb 23, 2013 at 1:41 | history | answered | Alexander Gruber | CC BY-SA 3.0 |