Right exact localizations of groups

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Right exact localizations of groups. / Akhtiamov, Danil ; Ivanov, Sergei O.; Pavutnitskiy, Fedor.

In: Israel Journal of Mathematics, Vol. 242, No. 2, 04.2021, p. 839-873.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{a0ccf2dfdc544d8abe962588b19133a9,

title = "Right exact localizations of groups",

abstract = "We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class of localizations which coincide with their zero derived functors. We call them right exact (in the sense of Keune). We prove that a right exact localization L preserves the class of nilpotent groups and that for a finite p-group G the map G → LG is an epimorphism. We also prove that some examples of localizations (Baumslag{\textquoteright}s P-localization with respect to a set of primes P, Bousfield{\textquoteright}s H R-localization, Levine{\textquoteright}s localization, Levine-Cha{\textquoteright}s ℤ-localization) are right exact. At the end of the paper we discuss a conjecture of Farjoun about Nikolov-Segal maps and prove a very special case of this conjecture.",

author = "Danil Akhtiamov and Ivanov, {Sergei O.} and Fedor Pavutnitskiy",

note = "Publisher Copyright: {\textcopyright} 2021, The Hebrew University of Jerusalem.",

year = "2021",

month = apr,

doi = "10.1007/s11856-021-2149-6",

language = "English",

volume = "242",

pages = "839--873",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Right exact localizations of groups

AU - Akhtiamov, Danil

AU - Ivanov, Sergei O.

AU - Pavutnitskiy, Fedor

PY - 2021/4

Y1 - 2021/4

N2 - We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class of localizations which coincide with their zero derived functors. We call them right exact (in the sense of Keune). We prove that a right exact localization L preserves the class of nilpotent groups and that for a finite p-group G the map G → LG is an epimorphism. We also prove that some examples of localizations (Baumslag’s P-localization with respect to a set of primes P, Bousfield’s H R-localization, Levine’s localization, Levine-Cha’s ℤ-localization) are right exact. At the end of the paper we discuss a conjecture of Farjoun about Nikolov-Segal maps and prove a very special case of this conjecture.

AB - We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class of localizations which coincide with their zero derived functors. We call them right exact (in the sense of Keune). We prove that a right exact localization L preserves the class of nilpotent groups and that for a finite p-group G the map G → LG is an epimorphism. We also prove that some examples of localizations (Baumslag’s P-localization with respect to a set of primes P, Bousfield’s H R-localization, Levine’s localization, Levine-Cha’s ℤ-localization) are right exact. At the end of the paper we discuss a conjecture of Farjoun about Nikolov-Segal maps and prove a very special case of this conjecture.

UR - http://www.scopus.com/inward/record.url?scp=85106487682&partnerID=8YFLogxK

U2 - 10.1007/s11856-021-2149-6

DO - 10.1007/s11856-021-2149-6

M3 - Article

AN - SCOPUS:85106487682

VL - 242

SP - 839

EP - 873

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -

ID: 90650941

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