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

2024/03/04 by Piwek, Paweł
#20D10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2403.02197

Abstract

We construct two finite groups of size 2³⁶⁵⋅ 3¹⁰⁵⋅ 7¹⁰⁴: 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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