On the conjugating representation of a finite group
Author:
K. L. Fields
Journal:
Proc. Amer. Math. Soc. 34 (1972), 35-37
MSC:
Primary 20C15
DOI:
https://doi.org/10.1090/S0002-9939-1972-0297889-9
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 
. 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.
- [1] Richard Brauer and K. A. Fowler, On groups of even order, Ann. of Math. (2) 62 (1955), 565–583. MR 74414, https://doi.org/10.2307/1970080
- [2] G. Frobenius and I. Schur, Über die reelen Darstellungen der endlichen Gruppen, S.-B. Preuss. Akad. Wiss. 1906, 186-208.
- [3] Louis Solomon, On the sum of the elements in the character table of a finite group, Proc. Amer. Math. Soc. 12 (1961), 962–963. MR 132783, https://doi.org/10.1090/S0002-9939-1961-0132783-8
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DOI:
https://doi.org/10.1090/S0002-9939-1972-0297889-9
Article copyright:
© Copyright 1972
American Mathematical Society
