# 2-layer

From Groupprops

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

## Definition

The **2-layer** of a group is defined as follows:

Let denote the full inverse image of the layer of via the natural projection . Here denotes the Brauer core of , viz the largest normal subgroup of odd order in .

The 2-layer of is denoted as or , and is defined as the subgroup obtained by repeated iteration of the operation.