Abstract. Let $n\geq3$. From the description of subdirectly irreducible complemented Arguesian lattices with four generators given by Herrmann, Ringel and Wille it follows that the subspace lattice of an $n$-dimensional vector space over a finite field is generated by four elements if and only if the field is a prime field. By exhibiting a 5-element generating set we prove that the subspace lattice of an $n$-dimensional vector space over an arbitrary finite field is generated by five elements.

AMS Subject Classification (1991): 06C05, 50D30, 14N20, 51D25

Keyword(s): Arguesian lattice, subspace lattice of a vector space, generating set of a subspace lattice

Received February 4, 2008, and in revised form February 8, 2008. (Registered under 6028/2009.)