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www.jeremykun.com | ||
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siddhartha-gadgil.github.io
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| | | | | [AI summary] The text discusses a formalization in Lean 4 of a mathematical result related to the group P and the unit conjecture. It outlines the construction of the group P as a metabelian group with a specific action and cocycle, the proof of its torsion freeness, and the use of decidable equality and enumeration to verify properties. The formalization also includes the construction of the group ring and the verification of Gardam's disproof of the unit conjecture by demonstrating the existence of a non-trivial unit in the group ring over the field F₂. | |
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terrytao.wordpress.com
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| | | | | This is yet another post in a series on basic ingredients in the structural theory of locally compact groups, which is closely related to Hilbert's fifth problem. In order to understand the s... | |
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mattbaker.blog
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| | | | | I'm teaching Graduate Algebra this semester, and I wanted to record here the proof I gave in class of the (existence part of the) structure theorem for finitely generated modules over a PID. It's a standard argument, based on the existence of the Smith Normal Form for a matrix with entries in a PID, but... | |
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mathematicaloddsandends.wordpress.com
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| | | I recently came across this theorem on John Cook's blog that I wanted to keep for myself for future reference: Theorem. Let $latex f$ be a function so that $latex f^{(n+1)}$ is continuous on $latex [a,b]$ and satisfies $latex |f^{(n+1)}(x)| \leq M$. Let $latex p$ be a polynomial of degree $latex \leq n$ that interpolates... | ||
