A close connection is uncovered between the lower central series of the free associative algebra of countable rank and the descending Loewy series of the direct sum of all Solomon descent algebras A" n € N o . Each irreducible A n -module is shown to occur in at most one Loewy section of any principal indecomposable A n -module. A precise condition for this occurrence and formulae for the Cartan numbers are obtained. 2000 Mathematics subject classification: primary 16N20; secondary 16D15, 16G10, 20C30, 05E15.