Timeline for Residual finiteness for modules over group rings
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| May 20, 2021 at 20:57 | comment | added | Alice | A datapoint: I definitely learned what a free product was as a student, but I only learned what a wreath product was far later in my career. I still find free products easier to think about. | |
| May 20, 2021 at 20:07 | comment | added | Benjamin Steinberg | @YCor, ok. The word easier is subjective so I dropped it. | |
| May 20, 2021 at 20:06 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| May 20, 2021 at 20:05 | comment | added | YCor | Actually I never learnt free groups or free products in university. Also when reading Hall's papers it looks like an exploration of infinite groups like going beyond finite groups, and the hierarchy of solvable groups was then very active. — I think by the way you should keep the answer (maybe just remove "easier"?) because it yields a wide variety of examples, and a result of independent interest. | |
| May 20, 2021 at 19:59 | comment | added | Benjamin Steinberg | @YCor, I guess you make a good point. I think of free groups as easy because most students learn about it in a first algebra course while few general algebra books mention wreath products. In any event a faithful simple module is much stronger than just having an infinite simple one. I guess I should delete this answer though. | |
| May 20, 2021 at 19:56 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| May 20, 2021 at 19:55 | comment | added | Benjamin Steinberg | @YCor, of course you are right and he puts that in parentheses right at the beginning of the paper. | |
| May 20, 2021 at 19:51 | comment | added | YCor | Note that in Formanek's result you certainly have to exclude the free product of two groups of order 2. | |
| May 20, 2021 at 19:50 | comment | added | YCor | What makes you believe that a free product is easier than a wreath product? In any case the module over the lamplighter group is mechanically a (non-faithful) module over the free group on 2 generators. | |
| May 20, 2021 at 19:47 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| May 20, 2021 at 19:41 | history | answered | Benjamin Steinberg | CC BY-SA 4.0 |