One-relator groups are a specific type of group characterized by a presentation that involves a single relator. This means that the group can be defined by a set of generators and one relation, typically expressed in the form 'G = <x_1, x_2, ..., x_n | r>', where 'r' is the relator. These groups are interesting because they exhibit properties that can be both complex and rich, making them significant in various classifications and problems related to group theory.
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