Cube map

From Groupprops
Jump to: navigation, search

Tihs article defines something that gives a well-defined function from every group to itself, that is invariant under group isomorphisms

Definition

Symbol-free definition

The cube map is a map from a group to itself that sends each element to its square.

Definition with symbols

The cube map on a group G is the map sending each x in G to x^3.

Facts

Endomorphism, surjective endomorphism, and automorphism

Image

Elements that lie in the image of the cube map are termed cube elements. When the order of the group is not a multiple of 3, then all elements are cube elements.