Timeline for Factorizable groups
Current License: CC BY-SA 4.0
27 events
| when toggle format | what | by | license | comment | |
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| Sep 26, 2021 at 22:00 | comment | added | Taras Banakh | @M.H.Hooshmand Ok, Thanks! | |
| Sep 26, 2021 at 18:43 | comment | added | M.H.Hooshmand | @ -Taras Banakh No problem, it was just for your information. | |
| Sep 26, 2021 at 13:52 | comment | added | Taras Banakh | @M.H.Hooshmand Yes, I have already noticed this. So, I asked this question the same year as the new edition of Kourovka appeared. Of course, I realize that the problem there were submitted earlier (maybe in 2014). So, I do not claim any priority, I was just curious (not being an expert in the field) about the status of those questions that lay essentially on a surface (but still have no full answer). | |
| Sep 25, 2021 at 19:46 | comment | added | M.H.Hooshmand | This question was asked in 2014 (see the above links), and then in The Kourovka Notebook2018. There are many published papers about it. | |
| Sep 25, 2021 at 19:34 | comment | added | M.H.Hooshmand | Also, see mathoverflow.net/questions/155986/factor-subset-of-finite-group. and The Kourovka Notebook (2018) Question 19.35. | |
| Sep 25, 2021 at 19:20 | comment | added | M.H.Hooshmand | See tandfonline.com/doi/abs/10.1080/… | |
| Mar 2, 2021 at 14:55 | history | edited | Taras Banakh | CC BY-SA 4.0 |
added 4 characters in body
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| Nov 30, 2018 at 15:18 | history | edited | Taras Banakh | CC BY-SA 4.0 |
edited body
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| Nov 28, 2018 at 22:25 | comment | added | Gro-Tsen | A priori, a minimal logarithmic signature (MLS) also allows for $|A_i|=4$ (since $2\times 2 = 2+2$). I don't remember whether this actually makes a difference for the existence of a MLS. | |
| Nov 28, 2018 at 19:44 | comment | added | Taras Banakh | @Gro-Tsen Thank you for the info. Indeed, the minimal logarithmic signature is a very interesting problem. It seems to be equivalent to the existence of a factorization $G=A_1\cdots A_n$ into subsets $A_i$ of prime cardinality $|A_i|$ such that $|A_1|\cdots|A_n|=|G|$. Right? | |
| Nov 28, 2018 at 18:13 | comment | added | Gro-Tsen | You might be interested in googling the keyword "minimal logarithmic signature" for a related problem which has come under some scrutiny in cryptography and on which some progress has been made. | |
| Nov 27, 2018 at 23:00 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Added info about the group $A_4$
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| Nov 27, 2018 at 6:17 | history | edited | Taras Banakh | CC BY-SA 4.0 |
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| Nov 26, 2018 at 19:33 | comment | added | Taras Banakh | @DerekHolt Exactly this reduction to the case of finite simple groups follows from Corollary. For a negative answer maybe it will be easier to construct a counterexample to this related question: mathoverflow.net/questions/316262/… | |
| Nov 26, 2018 at 19:21 | comment | added | Derek Holt | I would guess that if the answer to the question is yes, then it might be possible to prove it, given that the problem has been reduced to the case of finite simple groups, about which a lot is known. But if the answer to the question is no, then it could be very hard to prove because you have so many subsets to consider! | |
| Nov 26, 2018 at 19:03 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Added info about Farrokhi's observation.
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| Nov 26, 2018 at 18:32 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Replaced the definition of the bifactorizability by a more general one.
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| Nov 26, 2018 at 16:58 | answer | added | M. Farrokhi D. G. | timeline score: 7 | |
| Nov 26, 2018 at 16:12 | comment | added | Taras Banakh | @SamHopkins I am not expert in Group Theory. I admit that this problem has an answer, known to specialists, see the answer of M.Farrokhi D.G. | |
| Nov 26, 2018 at 16:08 | history | edited | Taras Banakh | CC BY-SA 4.0 |
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| Nov 26, 2018 at 16:01 | comment | added | Sam Hopkins | Amazing to me that this seemingly basic problem in the theory of finite groups is apparently open. | |
| Nov 26, 2018 at 15:54 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Modified the main theorem
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| Nov 26, 2018 at 14:56 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Added Problem 3
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| Nov 26, 2018 at 14:28 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Added a Theorem on alternating groups
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| Nov 26, 2018 at 13:57 | answer | added | M. Farrokhi D. G. | timeline score: 7 | |
| Nov 26, 2018 at 13:51 | history | edited | Taras Banakh | CC BY-SA 4.0 |
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| Nov 26, 2018 at 13:23 | history | asked | Taras Banakh | CC BY-SA 4.0 |