TY - JOUR

T1 - On lengths of Hℤ-localization towers

AU - Ivanov, Sergei O.

AU - Mikhailov, Roman

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85046752668&partnerID=8YFLogxK

U2 - 10.1007/s11856-018-1697-x

DO - 10.1007/s11856-018-1697-x

M3 - Article

AN - SCOPUS:85046752668

VL - 226

SP - 635

EP - 683

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -