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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiplicative subgroups of index three in a field


Authors: David B. Leep and Daniel B. Shapiro
Journal: Proc. Amer. Math. Soc. 105 (1989), 802-807
MSC: Primary 11T99
MathSciNet review: 963572
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Abstract: Theorem. If $ G$ be a subgroup of index 3 in the multiplicative group $ {F^*}$ of a field $ F$, then $ G + G = F$, except in the cases $ \left\vert F \right\vert = 4,7,13,{\text{or}}\,16$. The elementary methods used here provide a new proof of the classical case when $ F$ is finite.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0963572-X
PII: S 0002-9939(1989)0963572-X
Article copyright: © Copyright 1989 American Mathematical Society