Exponent of a group

This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition

The exponent of a group is defined as the least common multiple of the orders of all elements of the group. If there is no least common multiple, the exponent is taken to be infinity (or sometimes zero, depending on the convention).

Facts

• Exponent divides order in finite group: For a finite group, the exponent divides the order.
• Exponent of a finite group has precisely the same prime factors as order