Timeline for Results from abstract algebra which look wrong (but are true)
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2023 at 0:09 | comment | added | Michael | @GeoffRobinson, the way I would look at a question "is a finite simple group generated by 2 elements" would be like this: "take the first element, generate a cyclic subgroup with it, and act on it with commutators from the cyclic group generated by the other element; would the resulting set sufficiently dense, for the lack of a better word, in the given simple group to even suspect that it covers entire group?" And the intuitive answer would be "heck no". It is kind of amazing that you can always find two elements that defy that intuitive answer. | |
| Jan 20, 2023 at 18:48 | comment | added | Martin Brandenburg | This answer actually includes two WTF moments, one for each sentence. +1 | |
| Jan 20, 2023 at 16:43 | comment | added | Benjamin Steinberg | @GeoffRobinson, I guess I interpreted the question as statements where your first inclination would be to look for a coubterexample even if it is hard to find | |
| Jan 20, 2023 at 13:43 | comment | added | Benjamin Steinberg | @GeoffRobinson, my understanding is that the question is asking for examples where a property is too good to be true and there is no reason to believe expect it from the definitions but it turns out to be true. What in the definition of simple group seems to imply it should be generated by two elements? Infinite simple groups can require more than 2 generators. | |
| S Jan 19, 2023 at 23:42 | history | answered | Benjamin Steinberg | CC BY-SA 4.0 | |
| S Jan 19, 2023 at 23:42 | history | made wiki | Post Made Community Wiki by Benjamin Steinberg |