RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2019, Volume 105, Issue 4, Pages 553–563 (Mi mz11941)  

Quasirationality and Aspherical (Pro-$p$-) Presentations

A. Mikhovich

Lomonosov Moscow State University

Abstract: It is shown that the property of quasirationality of a (pro-$p$-) presentation of a (pro-$p$-) group $G$ is a property of the (pro-$p$-) group itself and does not depend on the choice of a presentation. It is proved that the class of quasirational presentations is wider than the class of aspherical pro-$p$-presentations (and of combinatorially aspherical presentations in the discrete case). For quasirational presentations, the notion of generalized permutationality of the module of relations is introduced, which turns out to be equivalent to the permutationality of the $\operatorname{mod}(p)$ quotient of the module.

Keywords: quasirationality, asphericity, generalized permutationality.

DOI: https://doi.org/10.4213/mzm11941

Full text: PDF file (489 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2019, 105:4, 550–558

Bibliographic databases:

UDC: 517
Received: 10.01.2018
Revised: 22.05.2018

Citation: A. Mikhovich, “Quasirationality and Aspherical (Pro-$p$-) Presentations”, Mat. Zametki, 105:4 (2019), 553–563; Math. Notes, 105:4 (2019), 550–558

Citation in format AMSBIB
\Bibitem{Mik19}
\by A.~Mikhovich
\paper Quasirationality and Aspherical (Pro-$p$-) Presentations
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 4
\pages 553--563
\mathnet{http://mi.mathnet.ru/mz11941}
\crossref{https://doi.org/10.4213/mzm11941}
\elib{http://elibrary.ru/item.asp?id=37180561}
\transl
\jour Math. Notes
\yr 2019
\vol 105
\issue 4
\pages 550--558
\crossref{https://doi.org/10.1134/S0001434619030283}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000467561600028}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065769654}


Linking options:
  • http://mi.mathnet.ru/eng/mz11941
  • https://doi.org/10.4213/mzm11941
  • http://mi.mathnet.ru/eng/mz/v105/i4/p553

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:158
    References:23
    First page:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020