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arXiv · 2403.02197

Solvable and non-solvable finite groups of the same order type

Paweł Piwek
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Abstract

We construct two finite groups of size $2^{365}\cdot 3^{105}\cdot 7^{104}$: a solvable group $G$ and a non-solvable group $H$, such that for every integer $n$ the groups have the same number of elements of order $n$. This answers a question posed in 1987 by John G. Thompson.

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Paweł Piwek. 2024-03-04. Solvable and non-solvable finite groups of the same order type. https://doi.org/10.2140/ant.2025.19.1663

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