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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


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.