Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C15

Retrieve articles in all journals with MSC: 20C15

Additional Information

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