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Generating Sets for Groups: due Wednesday October 30

1. Show that the subgroup of ℤ generated by two non-zero integers a and b is the cyclic subgroup generated by the greatest common divisor of a and b.
2. Show that D₄, the dihedral group of order 8 is generated by H, the reflection across the horizontal axis, and D', the reflection across the diagonal with slope one. Generalize to give two reflections that generate D_n.

Solution

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