Additive properties of multiplicative subgroups of finite index in fields
Author:
Pedro Berrizbeitia
Journal:
Proc. Amer. Math. Soc. 112 (1991), 365369
MSC:
Primary 12E99
MathSciNet review:
1057940
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Abstract: Gallai's theorem, an dimensional generalization of Van der Waerden's theorem on arithmetic progression, is used to prove the following theorem: Let be a field and a subgroup of finite index . There is a positive integer , which depends only on , so that if or , then .
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 R. L. Graham, Rudiments of Ramsey theory, Regional Conf. Ser. in Math., vol. 45, Amer. Math. Soc., Providence, RI, 1979. MR 608630 (82j:05018)
 [2]
 R. L. Graham, B. L. Rothschild, and J. H. Spencer, Ramsey theory, WileyInterscience, 1980. MR 591457 (82b:05001)
 [3]
 K. Ireland and M. Rosen, A classical introduction to modern number theory, SpringerVerlag, Berlin, 1982. MR 661047 (83g:12001)
 [4]
 A. Y. Khinchin, Three pearls of number theory, Rochester, NY, 1952, pp. 1117. MR 0046372 (13:724b)
 [5]
 D. B. Leep and D. B. Shapiro, Multiplicative subgroups of index three in a field, Proc. Amer. Math. Soc. 105 (1989), 802807. MR 963572 (89m:11127)
 [6]
 B. L. Van der Waerden, How the proof of Baudet's conjecture was found, Studies in Pure Mathematics (L. Mirsky, ed.), Academic Press, London, 1971, pp. 251260.
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DOI:
http://dx.doi.org/10.1090/S00029939199110579407
PII:
S 00029939(1991)10579407
Article copyright:
© Copyright 1991
American Mathematical Society
