Generating Sets for Groups: due Wednesday October 30

- 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*. - Show that
*D*_{4}, 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}