Abstract. In this paper we consider the Burnside problems for the class of Moufang and Bol loops. We show that a free finitely generated Moufang loop of exponent 3 is finite and that the orders of the finite 2-generated Bol loops of exponent 2 are not bounded.

AMS Subject Classification (1991): 20N05

Keyword(s): Burnside problem, Moufang loop, Bol loop, triality

Received November 15, 1999, and in revised form October 16, 2000. (Registered under 2810/2009.)