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    The quaternion group

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    Let G be a group generated by elements a and b such that |a| = 4, b^2 = a^2, and ba = a^3 b. Show that G is a group of order 8 and that G is isomorphic to the quaterunion group Q = {1, i, -1, -i, j, k, -j, -k }.

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    Solution Summary

    The multiplication table for the group is depicted.