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:
“You can’t have operations without screams. Pain and the knife—they’re inseparable.”
—Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)
“Go to the ant, thou sluggard; consider her ways, and be wise.”
—Bible: Hebrew Proverbs, 6:6.
The words were rendered by Samuel Johnson in the opening lines of The Ant: “Turn on the prudent ant thy heedful eyes, Observe her labours, sluggard, and be wise.”