A Counterexample to Huppert's Conjecture

Primarily AI-generated textHuman understanding: all partsmath.GR — Group Theory

Contributed by Shihao Wang ↗, Zhiwei Zheng ↗

Version 1 / Oct 26, 2026 / CC BY-SA 4.0

Abstract

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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