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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: 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 $\left \{ {{x_g}\left | {g \in G} \right .} \right \}$ 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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Keywords: Group determinant
Article copyright: © Copyright 1991 American Mathematical Society