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Proceedings of the American Mathematical Society

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Character values of finite groups as eigenvalues of nonnegative integer matrices


Author: David Chillag
Journal: Proc. Amer. Math. Soc. 97 (1986), 565-567
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1986-0840647-4
MathSciNet review: 840647
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Abstract: Let $ {C_1}$, $ {C_2}, \ldots $, $ {C_k}$ be the conjugacy classes of the finite group $ G$ and choose $ {x_i} \in {C_i}$, for $ i = 1$, $ 2, \ldots $, $ k$. For every complex character $ \theta $ of $ G$ there is a $ k \times k$ matrix $ M(\theta )$ whose entries are nonnegative integers such that $ {X^{ - 1}}M(\theta )X = {\text{diag}}(\theta ({x_1}),\theta ({x_2}), \ldots ,\theta ({x_k}))$ where $ X$ is the character table matrix of $ G$. Some consequences are shown.


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

  • [1] Z. Arad, D. Chillag and M. Herzog, Powers of characters of finite groups, J. Algebra (to appear) MR 860703 (87i:20013)
  • [2] H. F. Blichfeldt, A theorem concerning the invariants of linear homogeneous groups, with some applications to substitution-groups, Trans. Amer. Math. Soc. 5 (1904), 461-466. MR 1500684
  • [3] D. Chillag, Nonnegative matrices and products of characters and conjugacy classes in finite group, Publ. Math. Debrecen (to appear). MR 933394 (89b:20028)
  • [4] W. Feit, Representation theory of finite groups, North-Holland, 1982. MR 661045 (83g:20001)
  • [5] M. Kiyota, An inequality for finite permutation groups, J. Combin. Theory Ser. A 27 (1979), 119. MR 541348 (81f:20009)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0840647-4
Article copyright: © Copyright 1986 American Mathematical Society

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