Operations On Words
The product of two words is obtained by concatenation:
Even if the two words are reduced, the product may not be.
The inverse of a word is obtained by inverting each generator, and switching the order of the elements:
The product of a word with its inverse can be reduced to the empty word:
You can move a generator from the beginning to the end of a word by conjugation:
Read more about this topic: Word (group Theory)
Famous quotes containing the words operations and/or words:
“There is a patent office at the seat of government of the universe, whose managers are as much interested in the dispersion of seeds as anybody at Washington can be, and their operations are infinitely more extensive and regular.”
—Henry David Thoreau (1817–1862)
“But he knows the way that I take; when he has tested me, I shall come out like gold. My foot has held fast to his steps; I have kept his way and have not turned aside. I have not departed from the commandment of his lips; I have treasured in my bosom the words of his mouth.”
—Bible: Hebrew, Job 23:10-12.
Job, of God.