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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1991-1057940-7
MathSciNet review: 1057940
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Abstract: Gallai's theorem, an $ n$-dimensional generalization of Van der Waerden's theorem on arithmetic progression, is used to prove the following theorem:

Let $ F$ be a field and $ G \subseteq {F^ * }$ a subgroup of finite index $ n$. There is a positive integer $ N$, which depends only on $ n$, so that if $ {\text{Char}}F = 0$ or $ {\text{Char}}F \geq N$, then $ G - G = F$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1057940-7
Article copyright: © Copyright 1991 American Mathematical Society