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Direct Products and Isomorphisms

Let G = Z_3 direct product Z_3 direct product Z_3 and let H be the subgroup of SL(3, Z_3) consisting of

1 a b
the matrix H = { 0 1 c with a, b, c in Z_3 }
0 0 1

What is the order of G and H and are G and H isomorphic?

Solution Preview

Notice that G has order 3^3 = 27; the subgroup consists of matrices of the prescribed form (upper triangular, unit determinant), and ...

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Direct Products and Isomorphisms are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.