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A finite additive group is a finite group whose operation is written as addition. Its identity element is denoted $0$, the inverse element of $x$ is denoted $-x$, and translation $y\mapsto x+y$ is a bijection.

A group operation is the associative binary operation of a group. It has an identity element, and every element has an inverse element.

A group element has infinite order when no positive power of it is the identity element.