Group Generators

A set of generators (g_1,...,g_n) 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 G and a subset of elements (excluding the identity element) is connected iff the subset generates the group.

See also

Cayley Graph, Finitely Generated

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Arfken, G. "Generators." §4.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 261-267, 1985.

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Group Generators

Cite this as:

Weisstein, Eric W. "Group Generators." From MathWorld--A Wolfram Web Resource.

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