In this paper we show that a (non-abelian) free pro-p group cannot be obtai
ned as a closed subgroup of GL(n)(F), where F is a non-archimedean local he
ld and n is arbitrary. Using a theorem of E. I. Zel'manov we deduce some gr
oup theoretic properties of linear pro-p groups over a local field. Our mai
n tool is a recent theorem by Pink characterizing compact subgroups of GL(n
)(F). (C) 1999 Academic Press.