ON THE GENERALIZED NILPOTENT AND GENERALIZED SOLVABLE LOOPS -II

摘要

This paper studies the Frattini subloops of any loop and proves the equivalence of the following statements for a locally nilpotent loop Q: 1) Q is finitely generated; 2) Q satisfies the maximum condition for subloops; 3) Q satisfies the maximum condition for normal subloops. It also proves that the variety generated by a centrally nilpotent Moufang loop (or centrally nilpotent A-loop) is finitely based.