Finite groups with few character values

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Madanha, Sesuai Yasha

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Taylor and Francis

Abstract

A classical theorem on character degrees states that if a finite group has fewer than four character degrees, then the group is solvable. We prove a corresponding result on character values by showing that if a finite group has fewer than eight character values in its character table, then the group is solvable. This confirms a conjecture of T. Sakurai. We also classify non-solvable groups with exactly eight character values.

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Keywords

Almost simple groups, Character degrees, Character values

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Citation

Sesuai Y. Madanha (2022) Finite groups with few character values, Communications in Algebra, 50:1, 308-312, DOI: 10.1080/00927872.2021.1957107.