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## An analogue of Vosper's theorem for extension fields

Author
Bachoc, C.; Serra, O.; Zemor, G.
Type of activity
Journal article
Journal
Mathematical proceedings of the Cambridge Philosophical Society
Date of publication
2017-11-01
Volume
163
Number
3
First page
423
Last page
452
DOI
https://doi.org/10.1017/S0305004117000044
Repository
http://hdl.handle.net/2117/115387
https://arxiv.org/abs/1501.00602
URL
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/an-analogue-of-vospers-theorem-for-extension-fields/66AB475A5CF8C2DF2BC2BB0CC2AAED9D
Abstract
We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$\dim_FST =\dim_F S+\dim_F T-1,$$\end{linenomath} when dim FS, dim FT ¿ 2 and dim FST ¿ [L : F] - 2.
Citation
Bachoc, C., Serra, O., Zemor, G. An analogue of Vosper's theorem for extension fields. "Mathematical proceedings of the Cambridge Philosophical Society", 1 Novembre 2017, vol. 163, núm. 3, p. 423-452.
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics