Timeline for Occurrence problem for commutator subgroup
Current License: CC BY-SA 4.0
13 events
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| Jan 12, 2022 at 20:24 | comment | added | JBrude | Thank you very much for your answers. Anyway, I think that it is more specific than the membership/occurrence problem. As far as my knowledge, the membership/occurrence problem deals with finitely generated subgroups (arbitrary, given by generator as part of the input) and here the subgroup is fixed. I don't know if I should modify the name of the post or clarify this in any form. I am still interested in the answer. Regards! | |
| Dec 20, 2021 at 13:39 | history | edited | JBrude | CC BY-SA 4.0 |
added 203 characters in body
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| Dec 19, 2021 at 16:39 | comment | added | Benjamin Steinberg | @HJRW, no worries. That's where I learned the term but probably few people read the original paper where that terminology is used | |
| Dec 19, 2021 at 11:49 | comment | added | HJRW | @BenjaminSteinberg: You're right, I have cited that paper, and so I suppose I have brushed up against the terminology. Nevertheless, I wasn't aware of it, and didn't know what it meant. | |
| Dec 19, 2021 at 11:35 | comment | added | Benjamin Steinberg | @HJRW, you probably have cited the famous paper K.A. Mihailova, The occurrence problem for direct products of groups, Dokl. Akad. Nauk SSSR 119 (1958) 1103–1105 showing the generalized word problem is undecidable for a direct product of free groups :) but I think the terminology has not been commonly used in English for quite some time. Here is a sort of exception ams.org/journals/proc/1987-101-03/S0002-9939-1987-0908639-5/… but not very recent | |
| Dec 19, 2021 at 11:20 | comment | added | HJRW | @Carl-FredrikNybergBrodda: Perhaps, but I have been working on algorithmic problems in group theory for 18 years and have never heard the terminology before. So I think it's fair to say that it remains very unusual in English-language mathematical parlance. And note that there are many Russian mathematicians working in the Western mathematical community on algorithmic problems in group theory. | |
| Dec 19, 2021 at 11:17 | comment | added | HJRW | Note that the hypothesis that $G$ has solvable word problem is not needed for question 1 -- all that's needed is the (uniform) word problem in the abelianisation $G/[G,G]$, which is a finitely generated abelian group. | |
| Dec 19, 2021 at 3:00 | comment | added | Carl-Fredrik Nyberg Brodda | @YCor In the West, yes, but many Russian authors still use “occurrence problem” and historically it is this terminology which is always used there. | |
| Dec 19, 2021 at 1:15 | comment | added | YCor | By the way the usual terminology is "membership problem". | |
| Dec 18, 2021 at 20:52 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title; delete "thanks"
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| Dec 18, 2021 at 20:20 | comment | added | JBrude | Thank you @YCor for your reply. I still looking for the case when $H$ is de $k$-derived subgroup. I don't have a good reference to look for it, so any book or paper with this concrete topic is welcome. | |
| Dec 18, 2021 at 20:03 | comment | added | YCor | 1) Yes (assuming $G$ is meant to be finitely generated): more generally if $H$ is normal in $G$ and $G/H$ has solvable word problem then there's an algorithm, which is precisely the one solving the word problem in $H$. This applies to the derived subgroup, and also to the second derived subgroup. I don't know then, since there are f.g. solvable groups with non-solvable word problem. | |
| Dec 18, 2021 at 19:53 | history | asked | JBrude | CC BY-SA 4.0 |