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71 Visitor Messages

  1. Reply/View Conversation
    Hey Balarka,

    As far as I'm concerned, you are welcome to post such information in any thread no matter how old it is.
  2. Reply/View Conversation
    Hey, way to go!
  3. Reply/View Conversation
    Hey Balarka, thanks, glad you are enjoying the challenge! As for the origin of this particular problem, I'm not sure, I found it in https://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf (page 67, no solutions) and thought it was interesting. It only says "Japan 1990" so I'm guessing it's from a contest of some sort, yes (the second part of the challenge is a custom addition of mine).

    Your proof appears to be correct although I will need some time to look at it in more detail. My solution approaches the problem in a similar way as yours, but proceeds somewhat differently, though I have not fully checked mine either (I will post it in a week as per the forum rules, as well as a reference solution if I can find one)
  4. Reply/View Conversation
    Done. Let me know if you need to edit more things in the future.
  5. Reply/View Conversation
    Hey Balarka,

    topsquark was purposely given a wrong number and he wanted me to spot for the error, which it turns out, I was wrong. I guess I just am not good at math. Hehehe...
  6. Reply/View Conversation
    You should be able to edit it now. Let me know if there is a problem.
  7. Reply/View Conversation
    Hm, I'm interested in sending you a private message. Can you open up one space ?
  8. Reply/View Conversation
    I haven't had time to play with it, but it *is* interesting. The failure of right-exactness is what interests me: I suspect this is akin to why in groups left-split implies right-split, but not vice versa. So I would be tempted to investigate what a sufficient condition on $G$ would be so that the map: $Aut_N(G) \to Aut_N(H)$ is onto.

    I feel the center of $G$ will be relevant, here, so I would look at the two extremes: $G$ abelian, and $G$ with trivial center. I think outer automorphisms will be troublesome. On the other hand if $H$ is an extension of $N$, and $G$ is an extension of $H$, this might be fruitful (again, mimicking the field construction).

    For "concrete categories", for an object $A$ we can always form the group $Aut(A)$ of all isomorphisms $A \to A$. I can't say right off-hand if we can do so for ANY category, but this might be true (if our category is a poset, the automorphism groups are all trivial). So "some" generalization is possible, I'm not sure "how wide".
  9. Reply/View Conversation
    Yes, you are correct. The first post in a thread may be edited within 2 hours, and all other posts within 24 hours.

    However, if you run over the 24 hour limit, I will lift the limit for you temporarily since you are adding such great content.
  10. Reply/View Conversation
    Hey Balarka, according the the settings in the ACP it is 5 minutes.
Showing Visitor Messages 11 to 20 of 71
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About mathbalarka

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Date of Birth
January 12, 2000 (17)
About mathbalarka
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
Location:
West Bengal, India
Interests:
Number Theory
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India

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Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

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Name: Graduate POTW Award (Jul-Dec 2013)
Issue time: January 5th, 2014 16:52
Issue reason:
Math Help Boards