An analogue of Vosper's theorem for extension fields

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...

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Published in:Mathematical proceedings of the Cambridge Philosophical Society Vol. 163; no. 3; pp. 423 - 452
Main Authors: BACHOC, CHRISTINE, SERRA, ORIOL, ZÉMOR, GILLES
Format: Journal Article Publication
Language:English
Published: Cambridge, UK Cambridge University Press 01.11.2017
Subjects:
05 Combinatorics
05C Graph theory
60 Probability theory and stochastic processes
60C05 Combinatorial probability
Classificació AMS
Combinacions (Matemàtica)
Combinatorial analysis
Combinatorial probabilities
Combinatòria
Matemàtica discreta
Matemàtiques i estadística
Probabilitat
Subspaces
Theorems
Vector spaces
Àrees temàtiques de la UPC
ISSN:0305-0041, 1469-8064
Online Access:Get full text
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Summary: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.
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ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004117000044