Multiplicative subgroups of index three in a field

David B. Leep; Daniel B. Shapiro

doi:10.1090/S0002-9939-1989-0963572-X

Multiplicative subgroups of index three in a field

David B. Leep, Daniel B. Shapiro

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 ∣F∣ = 4 , 7 , 13, or 16. The elementary methods used here provide a new proof of the classical case when F is finite.

Original language	English
Pages (from-to)	802-807
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	105
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1989-0963572-X
State	Published - Apr 1989

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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title = "Multiplicative subgroups of index three in a field",

abstract = "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 ∣F∣ = 4 , 7 , 13, or 16. The elementary methods used here provide a new proof of the classical case when F is finite.",

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AU - Leep, David B.

AU - Shapiro, Daniel B.

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AB - 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 ∣F∣ = 4 , 7 , 13, or 16. The elementary methods used here provide a new proof of the classical case when F is finite.

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Multiplicative subgroups of index three in a field

Abstract

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