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Grooming among primates strengthens group bonds.
Literal
Primates [of-の] grooming [topic-は] group [of-の] bonds [object-を] strengthens.
毛づくろい ('grooming,' literally 'fur-making') is a compound noun for animal grooming — particularly the fur-cleaning behavior of social mammals. 集団の結合 ('group's bonds/unity') as the object. 強める is the transitive 'to strengthen' (paired with intransitive 強まる).