The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Alexander D. Rahm

doi:10.13025/15324

The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Alexander D. Rahm

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) disappears,we study a double cover of the amalgamated product decomposition SL2(Z)~=(Z/4Z)_(Z/2Z)(Z/6Z) inside SL2(Z[i]); and then compute the homology of the covering amalgam.

Original language	English (Ireland)
Journal	Journal Of Homotopy And Related Structures
DOIs	https://doi.org/10.13025/15324
Publication status	Published - 10 Feb 2013
Externally published	Yes

Access to Document

10.13025/15324Licence: CC BY-NC-ND

Defect of the Abelianization of the Picard groupAccepted author manuscript, 117 KBLicence: CC BY-NC-ND
Defect of the Abelianization of the Picard groupAccepted author manuscript, 117 KBLicence: CC BY-NC-ND

Cite this

@article{ee375f0879224acc81573096b60bd2e5,

title = "The subgroup measuring the defect of the Abelianization of SL\_2(Z[i])",

abstract = "There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) disappears,we study a double cover of the amalgamated product decomposition SL2(Z)\textasciitilde{}=(Z/4Z)\_(Z/2Z)(Z/6Z) inside SL2(Z[i]); and then compute the homology of the covering amalgam.",

author = "Rahm, \{Alexander D.\}",

year = "2013",

month = feb,

day = "10",

doi = "10.13025/15324",

language = "English (Ireland)",

journal = "Journal Of Homotopy And Related Structures",

issn = "1512-2891",

publisher = "Springer-Verlag",

}

TY - JOUR

T1 - The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

AU - Rahm, Alexander D.

PY - 2013/2/10

Y1 - 2013/2/10

N2 - There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) disappears,we study a double cover of the amalgamated product decomposition SL2(Z)~=(Z/4Z)_(Z/2Z)(Z/6Z) inside SL2(Z[i]); and then compute the homology of the covering amalgam.

AB - There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) disappears,we study a double cover of the amalgamated product decomposition SL2(Z)~=(Z/4Z)_(Z/2Z)(Z/6Z) inside SL2(Z[i]); and then compute the homology of the covering amalgam.

UR - http://hdl.handle.net/10379/3783

U2 - 10.13025/15324

DO - 10.13025/15324

M3 - Article

SN - 1512-2891

JO - Journal Of Homotopy And Related Structures

JF - Journal Of Homotopy And Related Structures

ER -

The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Abstract

Access to Document

Other files and links

Fingerprint

Cite this