Matrix powers over finite fields

Maria T. Acosta- De-Orozco and Javier Gomez-Calderon

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-5

Abstract:

Let G F ( q ) denote the finite field of order q = p e with p odd. Let M denote the ring of 2 × 2 matrices with entries in G F ( q ) . Let n denote a divisor of q − 1 and assume 2 ≤ n and 4 does not divide n . In this paper, we consider the problem of determining the number of n -th roots in M of a matrix B ∈ M . Also, as a related problem, we consider the problem of lifting the solutions of X 2 = B over Galois rings.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:462942

DOI: 10.1155/S0161171292000991

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