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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This article is about a term related to the Classification of finite simple groups
The layer of a group (sometimes also called commuting product) is defined in the following equivalent ways:
Definition with symbolsThe layer of a group , denoted is defined as: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
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 .