The group determinant determines the group
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- by Edward Formanek and David Sibley PDF
- Proc. Amer. Math. Soc. 112 (1991), 649-656 Request permission
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
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 649-656
- MSC: Primary 20C15; Secondary 15A15, 20C20
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062831-1
- MathSciNet review: 1062831