On lengths of Hℤ-localization towers

Sergei O. Ivanov, Roman Mikhailov

    Research output

    Abstract

    In this paper, the Hℤ-length of different groups is studied. By definition, this is the length of the Hℤ-localization tower or the length of the transfinite lower central series of Hℤ-localization. It is proved that, for a free noncyclic group, its Hℤ-length is ≥ ω+2. For a large class of ℤ[C]-modules M, where C is an infinite cyclic group, it is proved that the Hℤ-length of the semi-direct product M ⋊ C is ≤ ω + 1 and its Hℤ-localization can be described as a central extension of its pro-nilpotent completion. In particular, this class covers modules M, such that M⋊C is finitely presented and H2(M ⋊ C) is finite.

    Original languageEnglish
    Pages (from-to)635-683
    Number of pages49
    JournalIsrael Journal of Mathematics
    Volume226
    Issue number2
    DOIs
    Publication statusPublished - 1 Jun 2018

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    Lower Central Series
    Semi-direct product
    Module
    Central Extension
    Infinite Groups
    Cyclic group
    Free Group
    Completion
    Cover
    Class

    Scopus subject areas

    • Mathematics(all)

    Cite this

    Ivanov, Sergei O. ; Mikhailov, Roman. / On lengths of Hℤ-localization towers. In: Israel Journal of Mathematics. 2018 ; Vol. 226, No. 2. pp. 635-683.
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    On lengths of Hℤ-localization towers. / Ivanov, Sergei O.; Mikhailov, Roman.

    In: Israel Journal of Mathematics, Vol. 226, No. 2, 01.06.2018, p. 635-683.

    Research output

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