The subgroup measuring the defect of the Abelianization of SL_2(Z[i])
Date
2013-02-10Author
Rahm, Alexander D.
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A.D.Rahm (2013) 'The subgroup measuring the defect of the Abelianization of SL_2(Z[i])'. Journal of Homotopy and Related Structures.
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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.
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Journal article