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On a question of Feit

Authors: Pamela A. Ferguson and Alexandre Turull
Journal: Proc. Amer. Math. Soc. 97 (1986), 21-22
MSC: Primary 20C15
MathSciNet review: 831379
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Abstract: The following theorem is proved: Assume $ \chi $ is an irreducible complex character of the finite group $ G$ and $ G$ is $ \pi $-solvable where $ \pi $ is the set of prime divisors of $ \chi \left( 1 \right)$. Then $ f\left( \chi \right)$ contains an element of order $ f\left( \chi \right)$.

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

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  • [2] R. Brauer, A note on theorems of Burnside and Blichtfeldt, Proc. Amer. Math. Soc. 15 (1964), 31-34. MR 0158004 (28:1232)
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  • [4] I. Isaacs, Primitive characters, normal subgroups, and $ M$-groups, Math. Z. 177 (1981), 267-284. MR 612879 (82f:20026)

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Keywords: Prime character, $ \pi $-special character, $ f\left( \chi \right)$
Article copyright: © Copyright 1986 American Mathematical Society

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