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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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Keywords: Group determinant, character table, Brauer pairs
Article copyright: © Copyright 1993 American Mathematical Society

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