Relatively free, nearly nilpotent groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1972 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 11, pages 111-114 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Ivanyuta, I. D.;

doi: 10.1007/bf01097927

Relatively free, nearly nilpotent groups

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Abstract

We show that a free nilpotent group of countable rank, as well as a free group of countable rank of the variety defined by the identity [[x1 x2,..., xn], [xn+1, xn+2]]=1, satisfies the maximal condition for normal subgroups admitting endomorphisms induced by order preserving one-to-one mappings of the set of free generators into itself.

Related Organizations

Russian Academy of Sciences
Russian Federation

Keywords

Free nonabelian groups, Chains and lattices of subgroups, subnormal subgroups, Quasivarieties and varieties of groups

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