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I am aware that this series is incomplete, but it has a large body of existing content, and I am also aware that it is written to be "accessible to non-specialists", but that is obviously quite vague. All that really tells me is that I don't have to be a CFSG scholar, and on the other end that I can assume it's probably not, yknow, an undergraduate text. But what is the actual background needed to follow it? Group theory is a pretty vast field, and it is unclear to me whether GLS is written for people on the level of "grad students who took abstract algebra courses", "PhD candidates in group theory", or what.

Specifically the kind of answer I want is describing what the curriculum might look like for a hypothetical course whose purpose is GLS reading prep.

May Emerson
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  • For most of the postdocs and young professors working in group theory, if they have ever read any one volume of the series from cover to cover, it is the volume 3. And although the volume 3 does have brief introduction to algebraic groups, it is for reviewing and not intended for those who never saw the theory. So you should first learn some algebraic group theory, for example the Malle-Testerman book, then try to read volume 3. This is already a lot of work, and by then you should have some sense of prerequisites for the other volumes; most likely you will decide to not bother reading them. – Absol Nov 13 '23 at 04:41
  • I expected that might be the case. I set my sights on GLS because I am intrigued by the CFSG and frustrated by more accessible accounts of it failing to satisfy my questions of "okay, but why?" and the ongoing project to lay out the proof seems my best bet, but as you might suspect I only know basic group theory, so I would be far from the right level. I am very taken with abstract algebra, but I have not decided to dedicate myself to group theory, and it seems likely that I simply could never satisfy my questions without many years of study. I will at least look into algebraic group theory. – May Emerson Nov 13 '23 at 05:03
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    Algebraic group theory, especially the classification of finite groups of Lie type (which relies on the classification of simple algebraic groups) will be satisfying enough for you. The CFSG shows that if there is a simple group of minimal order which is not one of the alternating groups, the finite simple groups of Lie type, and the 26 known sporadic groups, then we eventually reach a contradiction. So the classification of Lie type is more "beautiful" than the rest of the proof. – Absol Nov 13 '23 at 09:30
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    Like the other comment I agree to get anywhere with GLS it would be helpful to understand some basics about groups of Lie type, algebraic groups, Lie algebras, etc. So books like Malle-Testerman, Carter, J. E. Humphreys, T. A. Springer, Steinberg's lecture notes, all cover some helpful background. – testaccount Nov 14 '23 at 01:38

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