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Solvability and Order Type for Finite Groups

Paweł Piwek

University of Oxford

Time: 16:00-17:00 (GMT+8), Wednesday March 26th, 2025
Location: Zoom


Abstract: How much can the order type — the list of element orders (with multiplicities) — reveal about the structure of a finite group \(G\)? Can it tell us whether \(G\) is abelian, nilpotent? Can it always determine whether \(G\) is solvable? This last question was posed in 1987 by John G. Thompson and I answered it negatively last year. The search for a counterexample was quite a puzzle hunt! It involved turning the problem into linear algebra and solving an integer matrix equation \(Ax=b\). This would be easy if not for the fact that the size of \(A\) was \(100,000\) by \(10,000\)…


Host: 张宝羽 Baoyu Zhang

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