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This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions

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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View a list of other standard non-basic definitions

This article is about a term related to the Classification of finite simple groups


Symbol-free definition

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

Definition with symbols

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

Relation with other subgroup-defining functions

Bigger subgroup-defining functions