Group generators are a set 
of group elements whose finite products, allowing inverse elements, produce every group
element in the group. Cyclic
groups can be generated as powers of a single generator.
A rotation that generates the cyclic
group of rotations, together with any reflection,
generates the dihedral group.
The Cayley graph of a group 
and a subset
of elements (excluding the identity
element) has a connected underlying undirected
graph iff the subset generates
the group.
