Assertion: abelian group's element | /r/HasProperty | its own inverse
Facets:
Source sentences:
text: Any such group is necessarily abelian because, since every element is its own inverse, xy = ( xy ) −1 = y
text: Because the order of the rows and columns of a Cayley table is in fact arbitrary, it is convenient to order them in the following manner: beginning with the group's identity element, which is always its own inverse, list first all the elements that are their own inverse, followed by pairs of inverses listed adjacent to each other.
text: all elements are their own inverses,
text: Show that if every element of the group G is its own inverse, then G is abelian.