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)
“We are all aware that speech, like chemistry, has a structure. There is a limited set of elements—vowels and consonants—and these are combined to produce words which, in turn, compound into sentences.”
—Roger Brown (b. 1925)