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

Alexander Rahm 1, *
* Corresponding author
Abstract : There is a natural inclusion of SL_2(Z) into SL_2(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 SL_2(Z) disappears, we study a double cover of the amalgamated product decomposition of SL_2(Z) as Z/(4Z) times Z/(6Z) amalgamated over Z/(2Z) inside SL_2(Z[i]); and then compute the homology of the covering amalgam.
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Submitted on : Thursday, January 17, 2013 - 2:23:20 PM
Last modification on : Friday, March 19, 2021 - 9:50:02 PM
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Alexander Rahm. The subgroup measuring the defect of the Abelianization of SL_2(Z[i]). Journal of Homotopy and Related Structures, Springer, 2013, pp.1-6. ⟨10.1007/s40062-013-0023-x⟩. ⟨hal-00777379⟩

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