Cube map

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


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.


Endomorphism, surjective endomorphism, and automorphism


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.