Explicit K₂ of some quotient rings of ℤ[G], G an elementary abelian p-group

2024/01/20 by Zhang, Yakun
#16S34 #19C20 #19C99 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2401.11210

Abstract

Let G be an elementary abelian p-group. We calculate K₂(ℤ[G]/I) for certain ideals I ⊆ ℤ[G] of the finite p-power index through computations of Dennis-Stein symbols. As an application, for p an odd prime, we give a complete description of the relative group SK₁(ℤ[G],p^kℤ[G]) and obtain more precise lower bounds of the prank of K₂(ℤ[G]) and Wh₂(G).

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