The introduction of the notion of group is an important milestone in the study of mathematics at the university level. This study focuses on how students respond to this notion, especially during the process of verifying commutativity. Commognitive Theoretical Framework has been used in order to identify, from a participationist perspective, how students use the metalevel rules to prove the given task. Results suggest that although the overall response to the given task is satisfactory, there have been identified two categories of errors. The first category is related to the proof that commutativity holds, indicating problematic object level understanding of the particular axiom. The second category is related to the process of proof per se indicating inherited problematic engagement with metarules.