2 research outputs found
An analogue of Vosper's Theorem for Extension Fields
We are interested in characterising pairs of -linear subspaces in a
field extension such that the linear span of the set of products of
elements of and of elements of has small dimension. Our central result
is a linear analogue of Vosper's Theorem, which gives the structure of vector
spaces in a prime extension of a finite field for which
when and .Comment: 33 page
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 vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}\end{linenomath} when dim FS, dim FT ¿ 2 and dim FST ¿ [L : F] - 2.Peer Reviewe