Let and let H be the subgroup of SL(3, Z3) consisting of (See Exercis...

Let and let H be the subgroup of SL(3, Z₃) consisting of

(See Exercise 48 in Chapter 2 for the definition of multiplication.) Determine the number of elements of each order in G and H. Are G and H isomorphic? (This exercise shows that two groups with the same number of elements of each order need not be isomorphic.)

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