By a simple combinatorial argument, and using a result of Brück, the Burnside problem is settled affirmatively for the class of Fischer 3-groups. 0. Introduction. In a recent book on cubic forms by Yu. I. Manin [1] the Burnside problem for the class of Fischer 3-groups was posed (cf. p. 39 of [1]). In this note we give a simple combinatorial argument leading to an affirmative settlement of this problem. A result of H. R. Brück [2] that every finitely generated commutative Moufang loop of period

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... 3 is finite, is essential to our proof. We also need some theorems connecting symmetric quasigroups, Moufang loops and Fischer groups.