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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ 2$-character table does not determine a group


Authors: Kenneth W. Johnson and Surinder K. Sehgal
Journal: Proc. Amer. Math. Soc. 119 (1993), 1021-1027
MSC: Primary 20C15
MathSciNet review: 1166358
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Abstract: Frobenius had defined the group determinant of a group $ G$ which is a polynomial in $ n = \vert G\vert$ 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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1166358-X
PII: S 0002-9939(1993)1166358-X
Keywords: Group determinant, character table, Brauer pairs
Article copyright: © Copyright 1993 American Mathematical Society