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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.

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Literature cited

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, USSR

    I. D. Ivanyuta

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  1. I. D. Ivanyuta
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 175–182, February, 1972.

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Ivanyuta, I.D. Relatively free, nearly nilpotent groups. Mathematical Notes of the Academy of Sciences of the USSR 11, 111–114 (1972). https://doi.org/10.1007/BF01097927

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  • DOI: https://doi.org/10.1007/BF01097927

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