Inequalities for finite group permutation modules
Authors:
Daniel Goldstein, Robert M. Guralnick and I. M. Isaacs
Journal:
Trans. Amer. Math. Soc. 357 (2005), 40174042
MSC (2000):
Primary 20B05; Secondary 20B15, 42A99
Published electronically:
May 25, 2005
MathSciNet review:
2159698
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: If is a nonzero complexvalued function defined on a finite abelian group and is its Fourier transform, then , where and are the supports of and . In this paper we generalize this known result in several directions. In particular, we prove an analogous inequality where the abelian group is replaced by a transitive right set, where is an arbitrary finite group. We obtain stronger inequalities when the set is primitive, and we determine the primitive groups for which equality holds. We also explore connections between inequalities of this type and a result of Chebotarëv on complex roots of unity, and we thereby obtain a new proof of Chebotarëv's theorem.
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 H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. MR 0183775 (32:1252)
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Additional Information
Daniel Goldstein
Affiliation:
Center for Communications Research, 4320 Westerra Ct., San Diego, California 92121
Email:
dgoldste@ccrwest.org
Robert M. Guralnick
Affiliation:
Department of Mathematics, University of Southern California, 1042 W. 36th Place, Los Angeles, California 90089
Email:
guralnic@math.usc.edu
I. M. Isaacs
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email:
isaacs@math.wisc.edu
DOI:
http://dx.doi.org/10.1090/S0002994705039279
PII:
S 00029947(05)039279
Received by editor(s):
October 24, 2003
Published electronically:
May 25, 2005
Additional Notes:
The research of the second author was partially supported by Grant DMS 0140578 of the U.S. NSF
The research of the third author was partially supported by the U.S. NSA
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
