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The Schur index and roots of unity

Author: G. J. Janusz
Journal: Proc. Amer. Math. Soc. 35 (1972), 387-388
MSC: Primary 20C05; Secondary 16A16
MathSciNet review: 0302748
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Abstract: A short proof is given for the main step in the proof of the theorem of Benard and Schacher which asserts that if the Schur index of a character $ \chi $ of a finite group is m then the mth roots of unity lie in the field of values $ Q(\chi )$.

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  • [1] C. Ford, Some results on the Schur index of a representation of a finite group, Canad. J. Math. 22 (1970), 626-640. MR 41 #5511. MR 0260891 (41:5511)
  • [2] M. Benard and M. Schacher, The Schur subgroup. II (to appear). MR 0302747 (46:1890)
  • [3] E. Witt, Die algebraische Strukture des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math. 190 (1952), 231-245. MR 14, 845. MR 0053944 (14:845a)

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Keywords: Crossed product, Schur index, Brauer group
Article copyright: © Copyright 1972 American Mathematical Society

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