Additive properties of multiplicative subgroups of finite index in fields
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- Proc. Amer. Math. Soc. 112 (1991), 365-369 Request permission
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 $G - G = F$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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