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 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 Dn.
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