In group theory, a branch of mathematics, each element in a group has the same number of cosets when considering a subgroup. More fundamentally, in a finite group, every element has the same order, which is the smallest positive integer \( n \) such that \( g^n = e \), where \( g \) is the element, and \( e \) is the identity element of the group.
Additionally, when discussing symmetries or transformations, each element can also be described in terms of having the same number of inverses. Each element \( g \) in a group has an inverse \( g^{-1} \) such that \( g \cdot g^{-1} = e \).
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