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 , , be the conjugacy classes of the finite group and choose , for , , . For every complex character of there is a matrix whose entries are nonnegative integers such that where is the character table matrix of . Some consequences are shown.

**[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