Layer

This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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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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This article is about a term related to the Classification of finite simple groups

Definition

Symbol-free definition

The layer of a group (sometimes also called commuting product) is defined in the following equivalent ways:

• It is the commuting product of all components
• It is the unique largest semisimple normal subgroup

Definition with symbols

The layer of a group $G$, denoted $E(G)$ is defined as: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

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Relation with other subgroup-defining functions

Bigger subgroup-defining functions

• Generalized Fitting subgroup: The generalized Fitting subgroup of a group is the product of its Fitting subgroup and the layer. In symbols $F^{*}(G)=F(G)E(G)$.