Definition:Complex (Group Theory)

Definition
Let $G$ be a group.

Let $K \subseteq G$ be a subset of $G$.

Then $K$ is referred to by some sources as a complex of elements of $G$.

Notation
The notation:
 * $K = A + B + C + \cdots$

can be seen for a complex whose elements are $A, B, C, \ldots$

Also known as
It is commonplace to refer to a complex in this context merely as a subset of $G$.

Hence the conventional language of set theory is used in this context: $K = \set {A, B, C, \ldots}$ for $K = A + B + C + \cdots$