The Chevalley-Warning theorem and a combinatorial question on finite groups
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- by B. Sury PDF
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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
- W. D. Gao - Two addition theorems on groups of prime order, J. Number Theory, Vol.56 (1996) 211-213.
- John E. Olson, On a combinatorial problem of Erdős, Ginzburg, and Ziv, J. Number Theory 8 (1976), no. 1, 52–57. MR 399032, DOI 10.1016/0022-314X(76)90021-4
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
- Received by editor(s): July 9, 1997
- Communicated by: David E. Rohrlich
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 951-953
- MSC (1991): Primary 20D60, 05E15, 11T06
- DOI: https://doi.org/10.1090/S0002-9939-99-04704-8
- MathSciNet review: 1476394