Group Generators
A set of generators 
is a set of group elements
such that possibly repeated application of the generators on themselves and each
other is capable of producing all the elements in the group. Cyclic
groups can be generated as powers of a single generator.
Two elements of a dihedral group that do not have
the same sign of ordering are generators for the entire group.
The Cayley graph of a group 
and a subset of
elements (excluding the identity element) is
connected iff the subset generates the group.
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