The $2$-character table does not determine a group
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- by Kenneth W. Johnson and Surinder K. Sehgal
- Proc. Amer. Math. Soc. 119 (1993), 1021-1027
- DOI: https://doi.org/10.1090/S0002-9939-1993-1166358-X
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Abstract:
Frobenius had defined the group determinant of a group $G$ which is a polynomial in $n = |G|$ variables. Formanek and Sibley have shown that the group determinant determines the group. Hoehnke and Johnson show that the $3$-characters (a part of the group determinant) determine the group. In this paper it is shown that the $2$-characters do not determine the group. If we start with a group $G$ of a certain type then a group $H$ with the same $2$-character table must form a Brauer pair with $G$. A complete description of such an $H$ is available in Comm. Algebra 9 (1981), 627-640.References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1021-1027
- MSC: Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1166358-X
- MathSciNet review: 1166358