Properties of Finite Groups
For finite groups, a "small neighborhood" is taken to be a subgroup defined in terms of a prime number p, usually the local subgroups, the normalizers of the nontrivial p-subgroups. A property is said to be local if it can be detected from the local subgroups. Global and local properties formed a significant portion of the early work on the classification of finite simple groups done during the 1960s.
Read more about this topic: Local Property
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