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The non-existence of block-transitive subspace designs

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https://doi.org/10.5070/C62156883Creative Commons 'BY' version 4.0 license
Abstract

Let q be a prime power and VFqd. A t-(d,k,λ)q design, or simply a subspace design, is a pair D=(V,B), where B is a subset of the set of all k-dimensional subspaces of V, with the property that each t-dimensional subspace of V is contained in precisely λ elements of B. Subspace designs are the q-analogues of balanced incomplete block designs. Such a design is called block-transitive if its automorphism group Aut(D) acts transitively on B. It is shown here that if t2 and D is a block-transitive t-(d,k,λ)q design then D is trivial, that is, B is the set of all k-dimensional subspaces of V.

Mathematics Subject Classifications: 05E18, 05B99

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