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* In the group generated by the symmetric difference on a (not necessarily finite) set, every element has order 2. Any such group is necessarily abelian because, since every element is its own inverse, xy = (xy)^-1 = y^-1x^-1 = yx. Such a group (also called a Boolean group), generalizes the Klein four-group example to an arbitrary number of components.
* (Z/pZ')ⁿ is generated by n elements, and n is the least possible number of generators.

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