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I am trying to write ~12 page paper on the construction of the Monster group. I have been thinking about this for a few weeks now, but every paper I read is a few levels ahead of my expertise with group theory, as I have only taken an introductory course to the subject (Abstract Algebra I). What are the core concepts that must be understood to be able to go through the construction of the monster?

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    $\begingroup$ Why are you writing a paper on the construction of something you don't know how to construct? $\endgroup$ May 5 '18 at 21:10
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    $\begingroup$ I think this is beyond what you can do at this stage of your education. You might be able to say something about the history of the sporadic groups. Start here (but don't stop here): en.wikipedia.org/wiki/Sporadic_group , en.wikipedia.org/wiki/Monster_group $\endgroup$ May 5 '18 at 21:13
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    $\begingroup$ @BrevanEllefsen: There are school systems that require students to do projects of the general shape "pick an advanced topic; find material to learn about it; write a paper presenting what you have learned". About 12 pages sounds like in the ballpark for that kind of thing. $\endgroup$ May 5 '18 at 21:15
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    $\begingroup$ @BrevanEllefsen: the obvious answer is "to learn how to construct it". Actually, it is fairly common for an honours seminar to consist precisely of that. $\endgroup$ May 5 '18 at 21:15
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    $\begingroup$ I attended John H Conway's Part III (graduate year) lectures on the construction of The Monster Group many years ago. 12 pages requires quite a lot of slick working, and assumption of non-trivial facts. See Conway and Sloane "Sphere Packings, Lattices and Groups" for something along these lines - chapter 29 in the 3rd edition is on my desk. If you understand what is going on there you will be able to do it. If you don't then you will need to grab hold of quite a lot of the previous 500 pages (and what is still assumed in an advanced text). It is worth understanding, but not trivial. $\endgroup$ May 5 '18 at 21:28

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