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Adjoint Transfer and Order-Lifting Dichotomies for 2 x 2 Matrices over Prime-Power Rings
For an odd prime p, we study the change in matrix order under lifting from Z/p^k Z to Z/p^(k+1) Z. The first variation of the order defect is an affine translate of a cyclic adjoint transfer on sl_2(F_p). We classify the full-order transfer for every q in GL_2(F_p): its rank is 3 for scalar elements
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