Simple group of Ree type

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This article defines a group property that can be evaluated, or makes sense, for simple groups


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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Definition

A simple group of Ree type is a finite simple non-Abelian group satisfying the following conditions:

  • It has an Abelian Sylow 2-subgroup
  • It contains an involution t such that

C_G(t) = <t> \times PSL(2,q)

where q > 5.

The case q = 5 corresponds instead to the Janko group (since PSL(2,5) = A_5).