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We characterize negative curvature of groups in terms of properties which can be checked locally in the Cayley graph. We prove the equivalence of these properties with the more familiar thin triangles property. We also present an algorithm which, when given a finite presentation of a group G , will recognize these properties in finite time if G is negatively curved.doi:10.2307/2161168 fatcat:nvs4yewxsvbjznnzvjaz2x4x6u