Free Group
The most general group generated by a set S is the group freely generated by S. Every group generated by S is isomorphic to a quotient of this group, a feature which is utilized in the expression of a group's presentation.
Read more about this topic: Generating Set Of A Group
Famous quotes containing the words free and/or group:
“Most men, even in this comparatively free country, through mere ignorance and mistake, are so occupied with the factitious cares and superfluously coarse labors of life that its finer fruits cannot be plucked by them. Their fingers, from excessive toil, are too clumsy and tremble too much for that.”
—Henry David Thoreau (1817–1862)
“Unless a group of workers know their work is under surveillance, that they are being rated as fairly as human beings, with the fallibility that goes with human judgment, can rate them, and that at least an attempt is made to measure their worth to an organization in relative terms, they are likely to sink back on length of service as the sole reason for retention and promotion.”
—Mary Barnett Gilson (1877–?)