Layer

From Groupprops
Jump to: navigation, search
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.
VIEW: Definitions built on this | Facts about this: (facts closely related to Layer, all facts related to Layer) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions

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:

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

Properties