Timeline for Is there any good methods for writing down basis for laws of groups?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 18, 2023 at 10:38 | comment | added | Benjamin Steinberg | I think actually one shows every finite group is contained in a cross variety and any subvariety of a cross variety is finitely based but I haven't looked at this kind of stuff in nearly 20 years | |
| May 18, 2023 at 10:31 | comment | added | Benjamin Steinberg | The identities satisfied by a direct product consists of those identities satisfied by both factors. But it is hard to see how you can extract a basis for this from a basis for each factor | |
| May 18, 2023 at 10:29 | comment | added | Benjamin Steinberg | I believe all the known proofs show that finite groups generate a Cross variety and then there is some general argument that cross varieties are finitely based so I think the proof doesn't really give something concrete and algorithmic. I think the nicest proof is in Kovacs and Newman, which can also be found in Hanna Neumann's book. | |
| May 18, 2023 at 10:12 | comment | added | Todor Antic | @DaveBenson Unfortunately Oates and Powell don't provide a general construction which is to be expected. It is hard to do in general, I was hoping that given a sufficiently nice description of a group, like finite presentation or as a product of two groups whose finite basis is already known, one would be able to construct the basis for the group at hand. This doesn't seem to be the case however. | |
| May 18, 2023 at 10:05 | comment | added | Dave Benson | Have you tried following through the proof in Oates and Powell, "Identical relations in finite groups", J Algebra 1 (1964), 11-39? It's also worth looking in MR for papers referring to this one, although most of them aren't about groups. I don't think there are any algorithms implemented in the usual algebra packages, and it's probably a hard problem in general. | |
| May 17, 2023 at 21:31 | comment | added | Benjamin Steinberg | I'm no expert but my feeling is no way way to get a finite basis is known | |
| S May 17, 2023 at 20:12 | review | First questions | |||
| May 18, 2023 at 0:33 | |||||
| S May 17, 2023 at 20:12 | history | asked | Todor Antic | CC BY-SA 4.0 |