Intuition
The purpose of defining a group homomorphism as it is, is to create functions that preserve the algebraic structure. An equivalent definition of group homomorphism is: The function h : G → H is a group homomorphism if whenever we have . In other words, the group H in some sense has a similar algebraic structure as G and the homomorphism h preserves that.
Read more about this topic: Group Homomorphism
Famous quotes containing the word intuition:
“All appeared new, and strange at first, inexpressibly rare and delightful and beautiful. I was a little stranger, which at my entrance into the world was saluted and surrounded with innumerable joys. My knowledge was divine. I knew by intuition those things which since my Apostasy, I collected again by the highest reason.”
—Thomas Traherne (1636–1674)
“Well, intuition isn’t much help in police work. Facts are what we need.”
—Crane Wilbur (1889–1973)