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Solvable and
nonsolvable finite groups of the same order type
Paweł Piwek |
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Vol. 19 (2025), No. 8, 1663–1670
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Abstract |
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We construct two groups of size : a solvable group and a nonsolvable group such that for every integer the groups have the same number of elements of order . This answers a question posed in 1987 by John G. Thompson. |
Keywords
Thompson's problem, order type
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Mathematical Subject Classification
Primary: 20D10
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Milestones
Received: 2 April 2024
Revised: 30 June 2024
Accepted: 3 September 2024
Published: 12 June 2025
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Authors |
| Paweł Piwek | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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