On subalgebras of free solvable and polynilpotent lie algebras

摘要

This paper investigates reduced free subalgebras of free solvable and free polynilpotent Lie algebras. A necessary and sufficient ondition is given for a subalgebra of a free solvable Lie algebra to be free solvable. An analoguous result is proved for free polynilpotent Lie algebras : If L i s a free polynilpotent, Lie algebra relative to a sequence n1,#x2026;,nkthen a subalgebra A is free polynilpotcnt if and only if it has I free generating set which is linearly independent and,generates a free nilpotent subalgebra of class r modulo some term Ln,#x2026;,niof the polycentral series of L, in which case A is free polynilpotent relative to the r+1 ni+1,#x2026;,nk.