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Generating set of a group
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==Free group== {{Main|Free group}} The most general group generated by a set <math>S</math> is the group [[free group|freely generated]] by <math>S</math>. Every group generated by <math>S</math> is [[isomorphic]] to a [[quotient group|quotient]] of this group, a feature which is utilized in the expression of a group's [[presentation of a group|presentation]].
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