Abstract
Let G be a finite group and \(\chi \in \text{ Irr }(G)\). The codegree of \(\chi \) is defined as \( {\text{ cod }}(\chi )=\frac{|G:\ker (\chi )|}{\chi (1)}\) and \( {\text{ cod }}(G)=\{ {\text{ cod }}(\chi ) \ |\ \chi \in \text{ Irr }(G)\}\) is called the set of codegrees of G. In this paper, we show that the set of codegrees of \( {\text{ PSL }}(3,q)\) and \( {\text{ PSU }}(3,q)\) determines the group up to isomorphism.
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Acknowledgements
Liu was supported by NSFC (Grant Nos. 11701421 and 11871011). Yang was supported by grants from the Simons Foundation (#499532 and #918096). The collaborative research was also funded by the American Mathematical Society’s Ky and Yu-Fen Fan Travel Grant Program. The authors are grateful to the referee for the valuable suggestions which greatly improved the manuscript.
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Liu, Y., Yang, Y. Huppert’s Analogue Conjecture for \( {\text{ PSL }}(3,q)\) and \( {\text{ PSU }}(3,q)\). Results Math 78, 7 (2023). https://doi.org/10.1007/s00025-022-01778-2
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DOI: https://doi.org/10.1007/s00025-022-01778-2