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Services. 2026-10-05 13:36:18 - Paul D. Foy - TheFormationGeneratedByAFiniteGroupUpdate I was perusing Claude the other day and I ventured into asking about what Claude knew of the recent developments in the area of mathematics, which is the formation generated by a finite group. It was reasonably up to date with things. It knew that things like the extension of a solvable group by a simple group had been established and it also knew of the counterexample which disproves the conjecture of Gaeschutz. It was very reserved, bless him, when it comes to the recent developments which I myself have undertaken. It was whinging on about the fact that this wasn't present in a peer-reviewed article, formally done, etc. , etc. , etc. Well I would, if I could. I made an attempt to apply to Leeds University to take up a post, which was advertised in Pure Mathematics, to formalise this area and to get this correct recognition and attribution, etc. That wasn't possible so I had to be content with publishing everything in books and by articles, which are readily available for an extremely modest amount. £30 will buy you all five articles and I don't know, is it £20 for the book? There you can establish that these things have actually been done. Now I've been doing these developments 2 years ago and I haven't looked much at the area since. My only motivation for these developments is not anybody else, unfortunately: no monetary reward, no reward of recognition, or anything. It's just self-satisfaction, which is running a bit thin nowadays because I've had to make do with nothing more than self-satisfaction for quite some time. Anyway we won't whinge on about that. I'll just say that Book 3 and Book 4 do the classification of finite groups which have finitely many subformations. For those of socle length 2 it's completely well established (that was established in Book 2) and I admit Book 3 is okay. Book 4 makes a big claim: you can't use the Bryant-Haerschenk theorem. You don't need to use the Bryant-Haerrschenk theorem. That's the big claim it makes. It makes that claim and I must admit the proof is a bit scrappy and a bit sketchy there. I doubt that would have survived peer review, but nevertheless it doesn't matter because I've fully sorted it out and I certainly do stand by these articles: a series of five articles which I've published online. They're all available in the bundle for a very modest price of £30. That would give me a bit of joy just to pass those on to some loving home, I think, but that's been denied me also because I've had no sales of them, no interest whatsoever. Claude, bless him, can exist in his state of ignorance. I'm not dismissing the efforts of Claude, etc. , to make knowledge available but he doesn't know everything and neither do I. That's what I have to say on that. Post a comment: |