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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The conjugation representation and fusionless extensions


Author: Edward Formanek
Journal: Proc. Amer. Math. Soc. 30 (1971), 73-74
MSC: Primary 20C15
MathSciNet review: 0291312
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Abstract: Let G be a finite group with center Z. G acts on itself by conjugation, and this induces a permutation representation P of $ G/Z$. It has been conjectured that every complex irreducible representation of $ G/Z$ occurs in P. This paper gives a counterexample to this conjecture.


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

  • [1] William Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. (2) 11 (1913), 40-42.
  • [2] Richard L. Roth, On the conjugating representation of a finite group, Pacific J. Math. 36 (1971), 515–521. MR 0289672 (44 #6860)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0291312-5
PII: S 0002-9939(1971)0291312-5
Keywords: Finite group, conjugation representation, permutation representation
Article copyright: © Copyright 1971 American Mathematical Society