The A-core and A-cover of a group

W. Chachólski; E. Damian; E. D. Farjoun; Y. Segev

doi:10.1016/j.jalgebra.2008.09.022

The A-core and A-cover of a group

W. Chachólski
, E. Damian
, E. D. Farjoun
, Y. Segev

Department of Mathematics

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

15 Scopus citations

Abstract

This paper provides a comprehensive investigation of the cellular approximation functor cell_A G, in the category of groups, approximating a group G by a group A. We also study related notions such as A-injection, A-generation and A-constructibility of a group G and we find several interesting connections with the Schur multiplier H₂ (G, Z). Our constructions are direct and are given in a slow and detailed manner.

Original language	English
Pages (from-to)	631-666
Number of pages	36
Journal	Journal of Algebra
Volume	321
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2008.09.022
State	Published - 15 Jan 2009

Keywords

A-cellular cover
A-constructibility
A-generation
A-injection
Central extensions
Schur multiplier

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2008.09.022

Cite this

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title = "The A-core and A-cover of a group",

abstract = "This paper provides a comprehensive investigation of the cellular approximation functor cellA G, in the category of groups, approximating a group G by a group A. We also study related notions such as A-injection, A-generation and A-constructibility of a group G and we find several interesting connections with the Schur multiplier H2 (G, Z). Our constructions are direct and are given in a slow and detailed manner.",

keywords = "A-cellular cover, A-constructibility, A-generation, A-injection, Central extensions, Schur multiplier",

author = "W. Chach{\'o}lski and E. Damian and Farjoun, \{E. D.\} and Y. Segev",

note = "Funding Information: E-mail addresses: [email protected] (W. Chach{\'o}lski), [email protected] (E.D. Farjoun), [email protected] (Y. Segev). 1 Partially supported by G{\"o}ran Gustafsson Stiftelse and VR grants 2002–2005 and 2005–2008. 2 Partially supported by the Israel Science Foundation grant No. 712/07, and by the center for advanced studies in Mathematics at Ben-Gurion University. 3 Partially supported by the Israel Science Foundation grant No. 712/07.",

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doi = "10.1016/j.jalgebra.2008.09.022",

language = "English",

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AU - Segev, Y.

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N2 - This paper provides a comprehensive investigation of the cellular approximation functor cellA G, in the category of groups, approximating a group G by a group A. We also study related notions such as A-injection, A-generation and A-constructibility of a group G and we find several interesting connections with the Schur multiplier H2 (G, Z). Our constructions are direct and are given in a slow and detailed manner.

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KW - A-cellular cover

KW - A-constructibility

KW - A-generation

KW - A-injection

KW - Central extensions

KW - Schur multiplier

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DO - 10.1016/j.jalgebra.2008.09.022

M3 - Article

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SP - 631

EP - 666

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

The A-core and A-cover of a group

Abstract

Keywords

ASJC Scopus subject areas

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