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On the problem of a finite basis of identities in groups

A. Yu. Ol'shanskii


Abstract: This paper contains a proof that the set of varieties of groups has the cardinality of the continuum. This implies the existence of an infinite system of group identities not equivalent to any finite system.

UDC: 519.4

MSC: 20E10, 03E10, 20E07, 20E36

Received: 14.10.1969

 English version: Mathematics of the USSR-Izvestiya, 1970, 4:2, 381–389

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