An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same.
Isomorphism Example #1
In this example, we show that the real numbers under addition are isomorphic to the group of positive real numbers under multiplication. This relationship dates back to the development of logarithms.
Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.