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In this paper we show that several classes of elementary properties (properties definable by sentences of a first order logic) of groups hold for all nonabelian free groups. These results are obtained by examining special embeddings of these groups into one another which preserve the properties in question.doi:10.1090/s0002-9947-1973-0320146-4 fatcat:nqdtakq76nex3dsajdohwciuli