In this article we study the low dimensional homology of the projective linear group PGL₂(A) over a GE₂-ring A. In particular, we prove a Bloch-Wigner type exact sequence over local domains. As applications we prove that H₂(PGL₂(A),Z[1/2]) K₂(A)[1/2] and H₃(PGL₂(A),Z[1/2]) K₃ⁱⁿᵈ(A)[1/2].
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Mirzaii et al. (2024) studied this question.
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