Tihs article defines something that gives a well-defined function from every group to itself, that is invariant under group isomorphisms
This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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The square map is a map from a group to itself that sends each element to its square.
Definition with symbols
The square map on a group is the map sending each in to .
Elements that lie in the image of the square map are termed square elements. When the group is of odd order, then all elements are square elements. Further information: kth power map is bijective iff k is relatively prime to the order