adelic groups

Adelic groups are mathematical structures that unify different ways of measuring and analyzing numbers, especially rational numbers, by considering all their possible completions simultaneously. This involves combining data from real numbers (like our everyday number line) and various p-adic numbers (which focus on divisibility by prime numbers) into a single framework. This global perspective allows mathematicians to study properties and relationships of numbers more comprehensively, making adelic groups a powerful tool in number theory and related fields. They act as a bridge connecting local properties (at individual primes) with global behavior across all numbers.