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  • Definition: If G is a group, a presentation of G consists of a family {x_i} of generators for G, along with a complete set {r_j} of relations for G, where each r_j is an element of the free group on the set {x_i}. If the family {x_i} is finite, then G is finitely generated, of course. If both the families {x_i} and {r_j} are finite, then G is said to be finitely presented, and these families form what is called a finite presentation for G.

    Source: Topology (second edition) by James R. Munkres

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