Local analysis
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In algebraic geometry and related areas of mathematics, local analysis is the practice of looking at a problem relative to each prime number p first, and then later trying to integrate the information gained at each prime into a 'global' picture. These are forms of the localization approach.
In group theory, local analysis was started by the Sylow theorems, which contain significant information about the structure of a finite group G for each prime number p dividing the order of G. This area of study was enormously developed in the quest for the classification of finite simple groups, starting with the Feit–Thompson theorem that groups of odd order are solvable.[1]