Additive properties of multiplicative subgroups of finite index in fields

Author:
Pedro Berrizbeitia

Journal:
Proc. Amer. Math. Soc. **112** (1991), 365-369

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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DOI:
https://doi.org/10.1090/S0002-9939-1991-1057940-7

Article copyright:
© Copyright 1991
American Mathematical Society