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  • Known and fixed gaps in the proof of the CFSG - MathOverflow
    Our overriding purpose has been to expound a coherent proof of CFSG that is supported completely by what we call ``Background Results,'' an explicit and restricted list of published books and papers, plus the assertion that every one of the $26$ sporadic groups is determined up to isomorphism, as a finite simple group, by its so-called centralizer-of-involution pattern
  • How do you *state* the Classification of finite simple groups?
    The second is how to state the CFSG that adequately reflects how human mathematicians think about it For the former question, one straightforward possibility for the sporadic groups, since we know their orders, is simply to state something like, "There exists a unique simple group, not in one of the aforementioned families, of each of the following orders: 7920, 95040," etc
  • Proof of CFSG assuming every simple group is two-generated
    This is very far from a justification of the fact that there would be a dramatic simplification of the proof of CFSG, and I clearly can't know what that person had in mind (perhaps it was something deeper and much more subtle), but it does at least point towards some potential simplifications if the two-generation of simple groups could be
  • gr. group theory - How much of the ATLAS of finite groups is . . .
    Namely, he said that a proof that relied on the CFSG and said so was ok, but a proof that relied on the ATLAS was not so ok, because the content has not been completely independently verified, and has as its basis old computer and other calculations that have only been done once
  • Revising the proof of CFSG - MathOverflow
    Once these were disposed of, group-theoretic methods, such as signalizers, became prevalent An exception is Glauberman's Z*-theorem, which used block theory, and still admits no proof without it This theorem was key to CFSG, and was one of the most cited papers in algebra in the 70s for that reason $\endgroup$ –
  • Where are the second- (and third-)generation proofs of the . . .
    In particular, he outlines the broad tactics that people are using in CFSG II, and some of the content that will be going into volume 7 Also, Inna Capdeboscq apparently gave an outline of volume 8, or at least a chunk of it, at the Asymptotic Group Theory conference in Budapest This was mentioned by Peter Cameron on his blog, sadly with no
  • Next steps on formal proof of classification of finite simple groups
    While people are steaming ahead on finessing the proof of the classification of finite simple groups (CFSG), we have a formal proof in Coq of one of the first major components: the Feit-Thompson odd-order theorem Note that the proof in Coq took a team, lead by Georges Gonthier, six years
  • gr. group theory - Highly transitive groups (without assuming the . . .
    Marshall Hall's The Theory of finite groups only cites an asymptotic bound: a permutation group of degree n that isn't S n or A n can be at most t-transitive for t less than 3 log n
  • Has anyone catalogued the first generation proof of the . . .
    Has anyone attempted to present an argument for the full CFSG, encoding the high level structure of the proof using journal references as necessary to establish the various subcases? That is, the part of the proof that was happening in the minds of specialists who felt comfortable declaring the problem "solved" after the last journal article had been published (Aschbacher-Smith Quasithin
  • gr. group theory - What are some interesting corollaries of the . . .
    For sporadic groups, it is trivial as (by CFSG) they are finite in number, and the statement is asymptotic For Lie groups they divide into small large fields, and use various results that might invoke the classification However, many of these various results similarly use the CFSG to get a uniform statement, with the bulk working as for Lie





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