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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 group determinant determines the group


Authors: Edward Formanek and David Sibley
Journal: Proc. Amer. Math. Soc. 112 (1991), 649-656
MSC: Primary 20C15; Secondary 15A15, 20C20
MathSciNet review: 1062831
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G = \left\{ {{g_1}, \ldots ,{g_n}} \right\}$ be a finite group of order $ n$, let $ K$ be a field whose characteristic is prime to $ n$, and let $ \left\{ {{x_g}\left\vert {g \in G} \right.} \right\}$ be independent commuting variables over $ K$. The group determinant of $ G$ is the determinant of the $ n \times n$ matrix $ \left( {{x_{{g_i}g_j^{ - 1}}}} \right)$. We show that two groups with the same group determinant are isomorphic.


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

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062831-1
PII: S 0002-9939(1991)1062831-1
Keywords: Group determinant
Article copyright: © Copyright 1991 American Mathematical Society