Timeline for Has the external knit product been used to construct a previously unknown group?
Current License: CC BY-SA 4.0
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| Apr 17, 2019 at 11:02 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Apr 16, 2019 at 22:11 | comment | added | Derek Holt | @GeoffRobinson It's worth pointing out it is still unknown whether the Kegel-Wielandt Theorem generalizes to infinite groups, although it has been proved in a number of special cases. | |
| Apr 16, 2019 at 21:07 | history | edited | John McVey | CC BY-SA 4.0 |
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| Apr 16, 2019 at 20:52 | comment | added | YCor | I've never seen any such construction. Actually I have always found all this "product" terminology a bit presumptuous and "exact factorization" (or "knit factorization") better reflects what it is. | |
| Apr 16, 2019 at 20:40 | comment | added | Geoff Robinson | There is a related kind of situation. I am thinking of the Kegel-Wielandt Theorem, which asserts that if a finite group $G$ has a factorization $G = AB$ with $A,B$ nilpotent, then $G$ is solvable. Here, one knows nothing else a priori about $G,$ except that it has a special factorization. This could be seen as a non--existence theorem (ie, a non-solvable group can't have such a factorization). While it is not assumed that $A \cap B = 1,$ the most interesting case is when $A$ and $B$ have coprime orders. | |
| Apr 16, 2019 at 20:28 | history | edited | John McVey | CC BY-SA 4.0 |
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| Apr 16, 2019 at 20:20 | history | asked | John McVey | CC BY-SA 4.0 |