Such groups were known for a long time before their abstract algebraic theory was developed according to the needs of major applications.
The reason for this distinction relates to general algebraic number theory.
A separate inspiration for F came from algebraic number theory.
Class field theory is the key part and the heart of algebraic number theory.
He is known for his work in the areas of automorphic forms, and algebraic number theory.
Almost any book on modern algebraic number theory, such as:
For more information about that: read algebraic number theory.
This is one of the main results of classical algebraic number theory.
Another example, playing a key role in algebraic number theory, is the field Q of p-adic numbers.
There are essentially two ways of generalising an algebraic theory.
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