Abstract
Let Fq = GF(q) denote the finite field of order q and F(m, q) the ring of m × m matrices over Fq. Let Ω be a group of permutations of Fq. If A, BϵF(m, q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A) = B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.
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