Multiplicative subgroups of finite index in a division ring
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- by Gerhard Turnwald PDF
- Proc. Amer. Math. Soc. 120 (1994), 377-381 Request permission
Abstract:
If $G$ is a subgroup of finite index $n$ in the multiplicative group of a division ring $F$ then $G - G = F$ or $|F| < {(n - 1)^4} + 4n$. For infinite $F$ this is derived from the Hales-Jewett theorem. If $|F| > {(n - 1)^2}$ and $- 1$ is a sum of elements of $G$ then every element of $F$ has this property; the bound ${(n - 1)^2}$ is optimal for infinitely many $n$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 377-381
- MSC: Primary 12E99; Secondary 05D10, 11T99, 12E15
- DOI: https://doi.org/10.1090/S0002-9939-1994-1215206-9
- MathSciNet review: 1215206