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Proceedings of the American Mathematical Society

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

 

 

On the conjugating representation of a finite group


Author: K. L. Fields
Journal: Proc. Amer. Math. Soc. 34 (1972), 35-37
MSC: Primary 20C15
MathSciNet review: 0297889
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Abstract: It is shown that the sum of the elements of the character table of a finite group is at least # conjugacy classes+ (# involutions-# classes of involutions)+(# real classes-# strongly real classes). Equality sometimes holds, e.g. for $ {A_5}$. Our investigations also demonstrate the appearance of a nontrivial real valued character (whose degree we can estimate) in the decomposition of the conjugating representation of a finite group possessing noncentral involutions.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0297889-9
Article copyright: © Copyright 1972 American Mathematical Society