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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An extension theorem for characters


Author: Stephen M. Gagola
Journal: Proc. Amer. Math. Soc. 83 (1981), 25-26
MSC: Primary 20C15; Secondary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0619973-5
MathSciNet review: 619973
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Abstract: If $ N$ is a normal subgroup of the finite group $ G$ and $ \psi $ is an irreducible complex character of $ N$ that is invariant in $ G$, then $ \psi $ is extendible to a character of $ G$ if $ (\left\vert {G:N} \right\vert,\left\vert N \right\vert/\psi (1)) = 1$


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

  • [1] Larry Dornhoff, Group representation theory. Part A: Ordinary representation theory, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 7. MR 0347959
    Larry Dornhoff, Group representation theory. Part B: Modular representation theory, Marcel Dekker, Inc., New York, 1972. Pure and Applied Mathematics, 7. MR 0347960
  • [2] I. Martin Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR 0460423

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619973-5
Article copyright: © Copyright 1981 American Mathematical Society