Simple group of component type

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This article defines a group property that can be evaluated, or makes sense, for simple groupsTemplate:Cfsg-group property


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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 finite simple non-Abelian group G is said to be a simple group of component type if for any involution t, the group C_G(t)/O(C_G(t)) has no quasisimple component.

Note that it does not matter which involution t we pick because the involutions of a group form a single conjugacy class.