## Properties of finite groups::Local property

### ::concepts

Locally::space Group::property Locally::local Finite::small Circle::subgroup Finitely::spaces**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.

**Local property sections**

Intro Properties of a single space Properties of a pair of spaces Properties of infinite groups Properties of finite groups Properties of commutative rings

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