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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 Chevalley-Warning theorem
and a combinatorial question on finite groups


Author: B. Sury
Journal: Proc. Amer. Math. Soc. 127 (1999), 951-953
MSC (1991): Primary 20D60, 05E15, 11T06
MathSciNet review: 1476394
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, W. D. Gao (1996) proved the following theorem: For a cyclic group $G$ of prime order, and any element $a$ in it, and an arbitrary sequence $g_1, \ldots, g_{2p-1}$ of $2p-1$ elements from $G$, the number of ways of writing $a$ as a sum of exactly $p$ of the $g_i$'s is $1$ or $0$ modulo $p$ according as $a$ is zero or not. The dual purpose of this note is (i) to give an entirely different type of proof of this theorem; and (ii) to solve a conjecture of J. E. Olson (1976) by answering an analogous question affirmatively for solvable groups.


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

  • [G] W. D. Gao - Two addition theorems on groups of prime order, J. Number Theory, Vol.56 (1996) 211-213.
  • [O] John E. Olson, On a combinatorial problem of Erdős, Ginzburg, and Ziv, J. Number Theory 8 (1976), no. 1, 52–57. MR 0399032 (53 #2883)

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Additional Information

B. Sury
Affiliation: School Of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Bombay 400 005 India
Email: sury@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04704-8
PII: S 0002-9939(99)04704-8
Keywords: Chevalley-Warning theorem, combinatorial group theory
Received by editor(s): July 9, 1997
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society