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 of prime order, and any element in it, and an arbitrary sequence of elements from , the number of ways of writing as a sum of exactly of the 's is or modulo according as 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.

**[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**

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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

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