On the orders of free groups of locally finite varieties

A. Yu. Ol'shanskii


Abstract: 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.

UDC: 519.4

MSC: 20E05, 20E10, 20E25

Received: 29.11.1971

 English version: Mathematics of the USSR-Izvestiya, 1973, 7:1, 85–90

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