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Primitive elements of the free groups of the varieties\mathfrak{A}\mathfrak{N}_n

Authors:	E I Timoshenko

Institution:	(1) Novosibirsk State Building Academy, Novosibirsk, USK

Abstract:	For groups of the formF/N', we find necessary and sufficient conditions for an elementg∈N/N' to belong to the normal closure of an elementh∈F/N'. It is proved that, in contrast to the case of a free metabelian group, for a free group of the variety $\mathfrak{A}\mathfrak{N}_2$ , there exists an elementh whose normal closure contains a primitive elementg, but the elementsh andg ^±1 are not conjugate. In the groupF( $\mathfrak{A}\mathfrak{N}_2$ ), two nonconjugate elements are chosen that have equal normal closures. Translated fromMaternaticheskie Zametki, Vol. 61, No. 6, pp. 884–889, June, 1997. Translated by A. I. Shtern

Keywords:	variety of groups free group of a variety primitive element normal closure theorem on freedom
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