Huppert's conjecture on groups determined by character degrees
Huppert's conjecture on groups determined by character degrees
Let be a finite group, and let 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 and are the same, then
where 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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