Huppert's conjecture on groups determined by character degrees

From papers

Let GG be a finite group, and let HH be a finite non-abelian simple group. Denote by the character degrees of a group the degrees of its complex irreducible characters. Huppert's conjecture. If the sets of character degrees of GG and HH are the same, then

GH×A,G \cong H \times A,

where AA is an abelian group. The conjecture asserts that non-abelian simple groups are essentially characterized by their sets of character degrees. The paper proves this conjecture for the almost simple groups with socle a small Ree group considered here, rather than resolving it in full generality.

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Sources & referencesView supporting material

Primary source

Seyed Hassan Alavi, “On groups with the same character degrees as almost simple groups with socle small Ree groups”, arXiv:2303.03607 (2023).

Additional references

7 papers in this index state this conjecture (2011–2023). The statement above is taken from the most recent of them; the others are arXiv:2108.09259, arXiv:1602.02168, arXiv:1601.06380, arXiv:1511.04129, arXiv:1105.4260, arXiv:1103.3937.

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