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Relations Subgroup

Definition: Given G, suppose we are given a family of generators {x_a}_(a in J) of generators for G. Let F be the the free group on the elements {x_a}. Then the obvious map h(x_a) = x_a of these elements into G extends to a homomorphism h: F > G that is surjective. If N equals the kernel of h, then F/N is isomorphic to G. So one way of specifying G is to give a family {x_a} of generators for G, and somehow to specify the subgroup N. Each element of N is called a relation on F, and N is called the relations subgroup.
Source: Topology (second edition) by James R. Munkres
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