Timeline for Classification of groups in which the centralizer of every non-identity element is cyclic
Current License: CC BY-SA 3.0
25 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2014 at 19:30 | answer | added | Marty Isaacs | timeline score: 12 | |
| Jan 25, 2014 at 19:35 | answer | added | Ian Agol | timeline score: 4 | |
| Jan 25, 2014 at 17:01 | answer | added | Geoff Robinson | timeline score: 11 | |
| Apr 27, 2013 at 14:11 | comment | added | Paul Taylor | Has it occurred to you all that Solovei might be (perhaps Russian and) not very confident in writing English? Could you not manage to be a little more accommodating towards him or her? | |
| Apr 27, 2013 at 10:29 | comment | added | Misha | Yemon: Oh, I see, I just misread your comment; now it all makes sense. | |
| Apr 27, 2013 at 6:39 | comment | added | Yemon Choi | Replying to Misha: solovei's comment just before mine asked the modified question about groups whete all centralizers of non-abelian elements are abelian, i.e. the commutative-transitive ones | |
| Apr 27, 2013 at 2:17 | history | reopened |
i. m. soloveichik Andy Putman R W Mariano Suárez-Álvarez Benjamin Steinberg |
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| Apr 26, 2013 at 22:39 | comment | added | i. m. soloveichik | @Stefan Ok. But I have already asked a revised question for the class of amenable groups. | |
| Apr 26, 2013 at 22:03 | comment | added | Stefan Kohl♦ | @solovei: I have tried to formulate your question in a more reasonable way -- please check whether you agree with the new formulation. | |
| Apr 26, 2013 at 22:02 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Tried to formulate the question in a more reasonable way.
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| Apr 26, 2013 at 21:15 | comment | added | Steve D | @Yemon: I think it is CA-groups? That is what was done by Suzuki, and Feit et al. picked up from there, classifying all CN-groups (centralizers are nilpotent). | |
| Apr 26, 2013 at 19:49 | comment | added | Andy Putman | @solovei : People would have reacted better if you had done two things. First, you should have phrased it as a question rather than as an imperative; as it was written, it "sounded" like homework. Second, you should have written a bit more. I'm fine with relatively terse questions, but this question needed more discussion than you gave. By the way, I voted to reopen. | |
| Apr 26, 2013 at 19:48 | comment | added | Misha | Lastly, read at least the wikipedia article on hyperbolic groups. | |
| Apr 26, 2013 at 19:47 | comment | added | Misha | @solovei: Your question was closed for several reasons: 1. The imperative tone of the question (making it sound like a hkw). 2. Unfocused nature of the question. In order to better formulate your questions, please, read mathoverflow.net/howtoask In particular, for questions like this, you should explain what "classify" means; maybe make a conjecture; state what you know about the problem, what did you try to solve it yourself, why are you interested in this, etc. Note also that the class of subgroups of GL(n,Z) is better than the class of all groups, but is still too large. | |
| Apr 26, 2013 at 19:24 | comment | added | i. m. soloveichik | Well the question is closed, although I don't know why. Was it too open-ended? should I have said characterize rather than classify? Would it have been better if I had restricted the class of groups? say to subgroups of GL_n(Z)? | |
| Apr 26, 2013 at 19:19 | comment | added | Misha | Yemon: Actually, CT is a weaker condition, which requires only centralizers to be abelian, not cyclic. Moreover, a complete classification of finite groups with cyclic centralizers is in the paper linked by Andy. I do not know what OP meant by his comment; maybe "infinite" instead of "finite". | |
| Apr 26, 2013 at 18:40 | comment | added | Yemon Choi | Re solovei's last comment, these are the finite CT groups (CT standing for commutative transitive). I think the relevant name here is Suzuki? | |
| Apr 26, 2013 at 18:17 | history | closed |
Andy Putman Felipe Voloch Steve Huntsman Martin Brandenburg Misha |
off topic | |
| Apr 26, 2013 at 18:04 | history | edited | user9072 |
edited tags
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| Apr 26, 2013 at 17:55 | comment | added | i. m. soloveichik | Andy, for finite groups I believe that groups where all centralizers are abelian can also be classified. | |
| Apr 26, 2013 at 17:39 | comment | added | Andy Putman | (the answer I gave is for finite groups. as Misha indicated, it is hopeless to answer it for infinite groups). | |
| Apr 26, 2013 at 17:37 | comment | added | Andy Putman | (comment about this being hw deleted, I realized that it is a little harder than I thought). This is answered in Theorem 10 of the following paper : rose-hulman.edu/math/MSTR/MSTRpubs/1991/RHIT-MSTR-1991-05.pdf | |
| Apr 26, 2013 at 17:28 | comment | added | i. m. soloveichik | that's a partial answer | |
| Apr 26, 2013 at 17:24 | comment | added | Misha | I suspect that the word "finite" is missing. Without the finiteness assumption, this is an utterly hopeless problem, for instance, all torsion-free hyperbolic groups will belong to this class. | |
| Apr 26, 2013 at 17:18 | history | asked | i. m. soloveichik | CC BY-SA 3.0 |