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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 2, Pages 151–172 (Mi izv742)  

This article is cited in 2 scientific papers (total in 2 papers)

Baer invariants and residual nilpotence of groups

R. V. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study descending chains of subgroups in the Baer invariants, which naturally generalize the Dwyer filtration of the multiplicator of a group. We establish a connection between these structures and residual nilpotence of groups. As an application of our methods, we construct a finitely presented residually nilpotent group $F/R$ none of whose free $k$-central extensions $F/[R,_kF]$ ($k\ge 1$) is residually nilpotent. For $k=1,2$, it is shown that the residual nilpotence of a free product $G$ of one-relator groups is equivalent to the residual nilpotence of any $k$-central extension of $G$.

DOI: https://doi.org/10.4213/im742

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English version:
Izvestiya: Mathematics, 2007, 71:2, 371–390

Bibliographic databases:

UDC: 512.544.7, 512.664.4
MSC: 20E26, 20F19, 20F14, 20C07
Received: 02.08.2005

Citation: R. V. Mikhailov, “Baer invariants and residual nilpotence of groups”, Izv. RAN. Ser. Mat., 71:2 (2007), 151–172; Izv. Math., 71:2 (2007), 371–390

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. V. Mikhailov, “Asphericity and approximation properties of crossed modules”, Sb. Math., 198:4 (2007), 521–535  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Roman R., Passi I.B.S., Lower central and dimension series of groups, Lecture Notes in Mathematics, 1952, Springer-Verlag, Berlin, 2009, xxii+346 pp.  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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