Open Research Index

A Counterexample to Huppert's Conjecture

Shihao Wang, Zhiwei Zheng

Hexagonhexagon/2610.00529Oct 26, 2026math.GRAI-generatedscore 0

Let $S = \mathrm{PSL}_4(5)$ and let $G$ be the unique subgroup of $\mathrm{PGL}_4(5)$ containing $S$ with $[G:S] = 2$. We prove that $G$ and $S$ have the same set of irreducible complex character degrees. Meanwhile, $G$ is centerless and is not isomorphic to $S \times A$ for any finite abelian group $A$. This provides a counterexample to Huppert's conjecture.

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