Geodesic
On the orders of free groups of locally finite varieties
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 85-90

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The results of [4] are used here to show that there exists a continuum of locally finite varieties of groups with pairwise distinct “ordinal” functions, thus disproving a conjecture of G. Higman. On the other hand, an example is given of distinct varieties having the same “ordinal” function. 
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A. Yu. Ol'shanskii. On the orders of free groups of locally finite varieties. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 85-90. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a2/