Inverses in group theory refer to the elements within a group that, when combined with a given element, yield the identity element of the group. This property is essential for the structure of a group, as it guarantees that every element has a corresponding counterpart that effectively 'undoes' its effect, reinforcing the closure and operation axioms of the group. Inverses play a crucial role in operations represented in Cayley tables, where the identity and inverse elements can be easily identified.
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