Definition: In mathematics, a nonidempotent element is an element that satisfies the property that for any two elements m and n in a group G, there exists a third element p such that mp = nm. In other words, if G has more than one element, then every non-idempotent element must be of order greater than 1. An example of a nonidempotent element is the identity element e of a group G. If G does not have any non-identity elements (
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