2-layer

This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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Definition

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

Let $E_{0}(G)$ denote the full inverse image of the layer of $G/O(G)$ via the natural projection $G\to G/O(G)$. Here $O(G)$ denotes the Brauer core of $G$, viz the largest normal subgroup of odd order in $G$.

The 2-layer of $G$ is denoted as $L(G)$ or $E_{0}^{\infty }(G)$, and is defined as the subgroup obtained by repeated iteration of the $E_{0}$ operation.